HOLOGRAPHIC

QUENCHES WITH A GAP

Esperanza Lopez

together with E. da Silva, J. Mas and A. Serantes, arXiv:1604. 08765

quantum quench

Quenches & revivals in holography

H0 , → H , |Ψ ⟩gs H0 |Ψ(t)⟩H

quantum quench

Quenches & revivals in holography

H0 , → H , |Ψ ⟩gs H0 |Ψ(t)⟩H

revival |Ψ(t+τ)⟩ ≃ |Ψ(t)⟩

holographic thermalization

quantum quench

Quenches & revivals in holography

H0 , → H , |Ψ ⟩gs H0 |Ψ(t)⟩H

revival |Ψ(t+τ)⟩ ≃ |Ψ(t)⟩

holographic thermalization

quantum quench

Quenches & revivals in holography

H0 , → H , |Ψ ⟩gs H0 |Ψ(t)⟩H

revival |Ψ(t+τ)⟩ ≃ |Ψ(t)⟩

holographic thermalization

reflecting boundary

bouncing geometries in AdS(Bizon, Rostworowski 2011; Buchel, Lehner, Liebling, 2012;......)

quantum quench

Quenches & revivals in holography

H0 , → H , |Ψ ⟩gs H0 |Ψ(t)⟩H

revival |Ψ(t+τ)⟩ ≃ |Ψ(t)⟩

holographic thermalization

reflecting boundary

bouncing geometries in AdS(Bizon, Rostworowski 2011; Buchel, Lehner, Liebling, 2012;......)

quantum quench

Quenches & revivals in holography

H0 , → H , |Ψ ⟩gs H0 |Ψ(t)⟩H

revival |Ψ(t+τ)⟩ ≃ |Ψ(t)⟩

↕ (Abajo, da Silva, Lopez, Mas, Serantes, 2014)

Outlook

holographic quenches: H ≠ H0

Outlook

holographic quenches: H ≠ H0

compare the parameter space for revivals and oscillating geometries

Outlook

holographic quenches: H ≠ H0

compare the parameter space for revivals and oscillating geometries

typical versus fine-tuned initial state and its holographic representation

Outlook

holographic quenches: H ≠ H0

compare the parameter space for revivals and oscillating geometries

typical versus fine-tuned initial state and its holographic representation

compare with results from other approaches: tensor networks

The model

quench dynamics of a 1+1 massive QFT

The model AdS boundary

IR hard wallAdS3 with an IR cutoff + massless scalar

quench dynamics of a 1+1 massive QFT

The model AdS boundary

IR hard wallAdS3 with an IR cutoff + massless scalar

D,N boundary conditions at the wall

quench dynamics of a 1+1 massive QFT

The model AdS boundary

IR hard wallAdS3 with an IR cutoff + massless scalar

D,N boundary conditions at the wall energy inflow from AdS boundary (Craps et al, 2013; Craps et al, 2014)

quench dynamics of a 1+1 massive QFT

The model AdS boundary

IR hard wallAdS3 with an IR cutoff + massless scalar

D,N boundary conditions at the wall energy inflow from AdS boundary (Craps et al, 2013; Craps et al, 2014)

quench dynamics of a 1+1 massive QFT

The model AdS boundary

IR hard wallAdS3 with an IR cutoff + massless scalar

energy is conserved at the IR wall

D,N boundary conditions at the wall energy inflow from AdS boundary (Craps et al, 2013; Craps et al, 2014)

quench dynamics of a 1+1 massive QFT

The model AdS boundary

IR hard wallAdS3 with an IR cutoff + massless scalar

energy is conserved at the IR wall time dependent profiles at the wall

redistribution of energy between metric and scalar

D,N boundary conditions at the wall energy inflow from AdS boundary (Craps et al, 2013; Craps et al, 2014)

quench dynamics of a 1+1 massive QFT

The model AdS boundary

IR hard wallAdS3 with an IR cutoff + massless scalar

energy is conserved at the IR wall time dependent profiles at the wall

redistribution of energy between metric and scalar

Δt < IR scale out of equilibrium

D,N boundary conditions at the wall energy inflow from AdS boundary (Craps et al, 2013; Craps et al, 2014)

quench dynamics of a 1+1 massive QFT

Static solutions with Φ=0

ds

2 =1z

2

✓�(1�M0z

2) dt

2 +dz

2

1�M0z2

+ dx

2

◆

Static solutions with Φ=0

AdS boundary: Minkowskids

2 =1z

2

✓�(1�M0z

2) dt

2 +dz

2

1�M0z2

+ dx

2

◆

Static solutions with Φ=0

AdS boundary: Minkowskids

2 =1z

2

✓�(1�M0z

2) dt

2 +dz

2

1�M0z2

+ dx

2

◆

M0=0 : AdS3

M0>0 : black hole

M0<0 : naked singularity

AdS-hard wall

Static solutions with Φ=0

AdS boundary: Minkowskids

2 =1z

2

✓�(1�M0z

2) dt

2 +dz

2

1�M0z2

+ dx

2

◆

M0=0 : AdS3

M0>0 : black hole

M0<0 : naked singularity

z0

AdS-hard wall

Static solutions with Φ=0

AdS boundary: Minkowskids

2 =1z

2

✓�(1�M0z

2) dt

2 +dz

2

1�M0z2

+ dx

2

◆

M0=0 : AdS3

M0>0 : black hole

M0<0 : naked singularity

z0

M0 z0 >1 : black hole2

AdS-hard wall

Static solutions with Φ=0

AdS boundary: Minkowskids

2 =1z

2

✓�(1�M0z

2) dt

2 +dz

2

1�M0z2

+ dx

2

◆

M0=0 : AdS3

M0>0 : black hole

M0<0 : naked singularity

z0

M0 z0 >1 : black hole2

M0 z0 <1 : AdS, AdS-BH, naked singularities2

AdS-hard wall

Static solutions with Φ=0

AdS boundary: Minkowskids

2 =1z

2

✓�(1�M0z

2) dt

2 +dz

2

1�M0z2

+ dx

2

◆

M0=0 : AdS3

M0>0 : black hole

M0<0 : naked singularity

z0

M0 z0 >1 : black hole2

M0 z0 <1 : AdS, AdS-BH, naked singularities2 M0: wall mass

AdS-hard wall

Static solutions with Φ=0

AdS boundary: Minkowskids

2 =1z

2

✓�(1�M0z

2) dt

2 +dz

2

1�M0z2

+ dx

2

◆

M0=0 : AdS3

M0>0 : black hole

M0<0 : naked singularity

z0

M0 z0 >1 : black hole2

M0 z0 <1 : AdS, AdS-BH, naked singularities2

no reason to exclude M0<0

M0: wall mass

AdS-hard wall

= 1

Static solutions with Φ=0

AdS boundary: Minkowskids

2 =1z

2

✓�(1�M0z

2) dt

2 +dz

2

1�M0z2

+ dx

2

◆

M0=0 : AdS3

M0>0 : black hole

M0<0 : naked singularity

z0

M0 z0 >1 : black hole2

M0 z0 <1 : AdS, AdS-BH, naked singularities2

no reason to exclude M0<0

M0: wall mass

Solitonic solutionsDirichlet bc at the wall :

static solutions with a non-trivial scalar profile

Solitonic solutionsDirichlet bc at the wall :

static solutions with a non-trivial scalar profile

solitons up to a threshold Φ0 (M0)

stable and unstable branches

stable solitons with M>1

given M0MXO\

0.2 0.4 0.6 0.8 1.0 1.2f0

0.2

0.4

0.6

0.8

1.0

1.2

•

•

:op dual to Φ

:total mass

Φ0 : scalar field at the wall

Solitonic solutionsDirichlet bc at the wall :

static solutions with a non-trivial scalar profile

-20 -15 -10 -5M0

-2

-1

1

2

f0parameter space

solitons up to a threshold Φ0 (M0)

stable and unstable branches

stable solitons with M>1

given M0MXO\

0.2 0.4 0.6 0.8 1.0 1.2f0

0.2

0.4

0.6

0.8

1.0

1.2

•

•

:op dual to Φ

:total mass

Φ0 : scalar field at the wall

Solitonic solutionsDirichlet bc at the wall :

static solutions with a non-trivial scalar profile

-20 -15 -10 -5M0

-2

-1

1

2

f0parameter space

boundary conditions can not be changed by bulk dynamics

solitons = vacua { M0 ,Φ0 } = couplings

solitons up to a threshold Φ0 (M0)

stable and unstable branches

stable solitons with M>1

given M0MXO\

0.2 0.4 0.6 0.8 1.0 1.2f0

0.2

0.4

0.6

0.8

1.0

1.2

•

•

:op dual to Φ

:total mass

Φ0 : scalar field at the wall

Mass gap

lowest pole of 2-point function

Mass gap

⇒ normal modes of Φlowest pole of 2-point function

Mass gap

⇒ normal modes of Φ

M0 ,Φ0 ≠ 0 break Lorentz invariance

field theory in a non-trivial homogeneous medium

lowest pole of 2-point function

Mass gap

⇒ normal modes of Φ

M0 ,Φ0 ≠ 0 break Lorentz invariance

field theory in a non-trivial homogeneous medium ≤ 1dωdk

causality

lowest pole of 2-point function

Mass gap

⇒ normal modes of Φ

M0 ,Φ0 ≠ 0 break Lorentz invariance

field theory in a non-trivial homogeneous medium ≤ 1dωdk

causality

lowest pole of 2-point function

mgap = ω| for the lowest normal modek=0

Mass gap

⇒ normal modes of Φ

M0 ,Φ0 ≠ 0 break Lorentz invariance

field theory in a non-trivial homogeneous medium ≤ 1dωdk

causality

lowest pole of 2-point function

M0=1/2

M0=-8

the gap increases with negative M0, closes up with growing Φ0

mgap = ω| for the lowest normal modek=0

Entanglement entropy

A

B

S(A)= - Tr ρA log ρA

Entanglement entropy

A

B

Area law

S(A)∝ ∂A

S(A)= - Tr ρA log ρA

Entanglement entropy

A

B

Area law

S(A)∝ ∂A

ξ : correlation length

S(A)= - Tr ρA log ρA

Entanglement entropy

A

B

Area law

S(A)∝ ∂A

ξ : correlation length

1+1 gapped theory

• •l

S(A)= - Tr ρA log ρA

Entanglement entropy

A

B

Area law

S(A)∝ ∂A

ξ : correlation length

1+1 gapped theory

• •l

S(l>ξ ) = const

S(A)= - Tr ρA log ρA

Entanglement entropy

A

B

Area law

S(A)∝ ∂A

ξ : correlation length

1+1 gapped theory

• •l

S(l>ξ ) = const

l homologous to γS(l )∝ length(γ)

holographic entanglement entropy

γ

IR wall

• •l

(Ryu, Takayanagi, 2006)

S(A)= - Tr ρA log ρA

Entanglement entropy

A

B

Area law

S(A)∝ ∂A

ξ : correlation length

1+1 gapped theory

• •l

homology relative to IR wall

S(l>ξ ) = const

l homologous to γS(l )∝ length(γ)

holographic entanglement entropy

γ

IR wall

• •l

(Ryu, Takayanagi, 2006)

S(A)= - Tr ρA log ρA

Entanglement entropy

A

B

Area law

S(A)∝ ∂A

ξ : correlation length

1+1 gapped theory

• •l

homology relative to IR wall

S(l>ξ ) = const

l homologous to γS(l )∝ length(γ)

holographic entanglement entropy

γ

IR wall

• •l

(Ryu, Takayanagi, 2006)

S(A)= - Tr ρA log ρA

Entanglement entropy

A

B

Area law

S(A)∝ ∂A

ξ : correlation length

1+1 gapped theory

• •l

homology relative to IR wall

S(l>ξ ) = const

pure state S(A)=S(B) in the absence of horizons: pure states

l homologous to γS(l )∝ length(γ)

holographic entanglement entropy

γ

IR wall

• •l

(Ryu, Takayanagi, 2006)

S(A)= - Tr ρA log ρA

Correlation length

γγ

ll

Correlation length

S(l )∝log(l )

γγ

ll

Correlation length

S(l )∝log(l ) S(l )=const

γγ

ll

Correlation length

S(l )∝log(l ) S(l )=const

ξ length(con)=length(dis) γγ

ll

Correlation length

S(l )∝log(l ) S(l )=const

ξ length(con)=length(dis) γγ

ll

M0=1/2

M0=-8

ξ decreases with negative M0, increases with Φ0

Correlation length

S(l )∝log(l ) S(l )=const

ξ length(con)=length(dis) γγ

ll

expected: mgap ξ = O(1)

M0=1/2

M0=-8

ξ decreases with negative M0, increases with Φ0

Correlation length

S(l )∝log(l ) S(l )=const

ξ length(con)=length(dis) γγ

ll

expected: mgap ξ = O(1)

except close to soliton threshold:large N effect

M0=1/2

M0=-8

◉

0.0 0.5 1.0 1.5 2.0f0

1

2

3

4

5

6

7

xw

M0=-∞

M0=1/2

M0=-8

ξ decreases with negative M0, increases with Φ0

Holographic quench

simple gapped model with 2 couplings, which control IR physics

ds

2 =1z

2

✓�A(t, z)e�2�(t,z)

dt

2 +dz

2

A(t, z)+ dx

2

◆, �(t, z)

⇧0 =

✏

↵

1

cosh

2 t/↵

Holographic quench

simple gapped model with 2 couplings, which control IR physics

ds

2 =1z

2

✓�A(t, z)e�2�(t,z)

dt

2 +dz

2

A(t, z)+ dx

2

◆, �(t, z)

ds

2 =1z

2

✓�A(t, z)e�2�(t,z)

dt

2 +dz

2

A(t, z)+ dx

2

◆, �(t, z)

⇧0 =

✏

↵

1

cosh

2 t/↵

Holographic quench

simple gapped model with 2 couplings, which control IR physics

ds

2 =1z

2

✓�A(t, z)e�2�(t,z)

dt

2 +dz

2

A(t, z)+ dx

2

◆, �(t, z)

ds

2 =1z

2

✓�A(t, z)e�2�(t,z)

dt

2 +dz

2

A(t, z)+ dx

2

◆, �(t, z)

⇧0 =

✏

↵

1

cosh

2 t/↵

dirichlet bc : �̇0 = 0

Holographic quench

simple gapped model with 2 couplings, which control IR physics

ds

2 =1z

2

✓�A(t, z)e�2�(t,z)

dt

2 +dz

2

A(t, z)+ dx

2

◆, �(t, z)

ds

2 =1z

2

✓�A(t, z)e�2�(t,z)

dt

2 +dz

2

A(t, z)+ dx

2

◆, �(t, z)

⇧0 =

✏

↵

1

cosh

2 t/↵

⇧ ⌘ A�1e��̇

⇧0 =

✏

↵

1

cosh

2 t/↵ → time dependent wall profile : dirichlet bc : �̇0 = 0

Holographic quench

simple gapped model with 2 couplings, which control IR physics

ds

2 =1z

2

✓�A(t, z)e�2�(t,z)

dt

2 +dz

2

A(t, z)+ dx

2

◆, �(t, z)

ds

2 =1z

2

✓�A(t, z)e�2�(t,z)

dt

2 +dz

2

A(t, z)+ dx

2

◆, �(t, z)

⇧0 =

✏

↵

1

cosh

2 t/↵

⇧ ⌘ A�1e��̇

⇧0 =

✏

↵

1

cosh

2 t/↵ → time dependent wall profile :

M = M0 + MΦ = const

⤷

⤶

energy exchange

dirichlet bc : �̇0 = 0

ËË

-12 -10 -8 -6 -4 -2M0

-2

-1

1

2

f0

◉

shorter time span

initial state

growing amplitude

Holographic quench

simple gapped model with 2 couplings, which control IR physics

ds

2 =1z

2

✓�A(t, z)e�2�(t,z)

dt

2 +dz

2

A(t, z)+ dx

2

◆, �(t, z)

ds

2 =1z

2

✓�A(t, z)e�2�(t,z)

dt

2 +dz

2

A(t, z)+ dx

2

◆, �(t, z)

⇧0 =

✏

↵

1

cosh

2 t/↵

⇧ ⌘ A�1e��̇

⇧0 =

✏

↵

1

cosh

2 t/↵ → time dependent wall profile :

M = M0 + MΦ = const

⤷

⤶

energy exchange

M<1 : ever bouncing

dirichlet bc : �̇0 = 0

ËË

-12 -10 -8 -6 -4 -2M0

-2

-1

1

2

f0

◉

shorter time span

initial state

growing amplitude

Revivals versus bounces

when to expect revivals? interactions disfavor revivals, except

Revivals versus bounces

when to expect revivals? interactions disfavor revivals, except

energy density < ( infrared scale )

# fieldsd

Revivals versus bounces

when to expect revivals? interactions disfavor revivals, except

energy density < ( infrared scale )

# fieldsd

global AdS # fields ~ 1/G , infrared scale ~ 1/R M R < 1d

Revivals versus bounces

when to expect revivals? interactions disfavor revivals, except

energy density < ( infrared scale )

# fieldsd

global AdS # fields ~ 1/G , infrared scale ~ 1/R M R < 1d

AdS3 hard wall

Mcollapse : mass leading to horizon formation for bc {M0 ,Φ0}

Revivals versus bounces

when to expect revivals? interactions disfavor revivals, except

energy density < ( infrared scale )

# fieldsd

global AdS # fields ~ 1/G , infrared scale ~ 1/R M R < 1d

√Mcollapse - Mgs ≲ infrared scale

AdS3 hard wall

Mcollapse : mass leading to horizon formation for bc {M0 ,Φ0}

Revivals versus bounces

when to expect revivals? interactions disfavor revivals, except

energy density < ( infrared scale )

# fieldsd

global AdS # fields ~ 1/G , infrared scale ~ 1/R M R < 1d

√Mcollapse - Mgs ≲ infrared scale

AdS3 hard wall

Mcollapse : mass leading to horizon formation for bc {M0 ,Φ0}

M0=-∞◉

M0=-8

M0=1/2

0.5 1.0 1.5 2.0f0

0.1

0.2

0.3

0.4

0.5

DM êw

Decoding oscillating geometriesassociated field theory state mechanism behind revivals

Decoding oscillating geometriesassociated field theory state mechanism behind revivals

parameters of the wall action : α (time span), ε (amplitude)

Decoding oscillating geometriesassociated field theory state mechanism behind revivals

parameters of the wall action : α (time span), ε (amplitude)

α = √gtt α~ __↓

Decoding oscillating geometriesassociated field theory state mechanism behind revivals

parameters of the wall action : α (time span), ε (amplitude)

α = √gtt α~ __↓

α >1: adiabatic change~-20 -15 -10 -5M0

-2

-1

1

2

f0

-20 -15 -10 -5M0

-2

-1

1

2

f0

⤴••

Decoding oscillating geometriesassociated field theory state mechanism behind revivals

parameters of the wall action : α (time span), ε (amplitude)

α = √gtt α~ __↓

α >1: adiabatic change~-20 -15 -10 -5M0

-2

-1

1

2

f0

-20 -15 -10 -5M0

-2

-1

1

2

f0

⤴••

α <1: radial localization~

MΦ=∫ρdz

Decoding oscillating geometriesassociated field theory state mechanism behind revivals

parameters of the wall action : α (time span), ε (amplitude)

α = √gtt α~ __↓

α >1: adiabatic change~-20 -15 -10 -5M0

-2

-1

1

2

f0

-20 -15 -10 -5M0

-2

-1

1

2

f0

⤴••

α <1: radial localization~

MΦ=∫ρdz

α ≈1: standing wave~

α = 0.8

α = 0.2

Energy density

M-Mgs

M-Mgse = _

energy density above vacuum normalized to that for fast

thermalization

Energy density

M-Mgs

M-Mgse = _

energy density above vacuum normalized to that for fast

thermalization

α ≈ 1: e ≪ 1

α < 1: e ≲ 1~

~

Energy density

M-Mgs

M-Mgse = _

energy density above vacuum normalized to that for fast

thermalization

α ≈ 1: e ≪ 1

α < 1: e ≲ 1~

~

Periodicity

α ≈ 1: periodicity of lowest normal mode

~2πωτ ≈

Energy density

M-Mgs

M-Mgse = _

energy density above vacuum normalized to that for fast

thermalization

α ≈ 1: e ≪ 1

α < 1: e ≲ 1~

~

Periodicity

α ≈ 1: periodicity of lowest normal mode

~2πωτ ≈

α < 1: different periodicity~

larger far from stability threshold

Tensor networks

variational ansatz for QFT states based on entanglement properties

• ↑↓| i =X

ci1i2. . . iN |i1i2. . . iN i • • ••• • ••• ••••

Tensor networks

variational ansatz for QFT states based on entanglement properties

• ↑↓| i =X

ci1i2. . . iN |i1i2. . . iN i

matrix product states ci1i2. . . iN = Tr Ai1Ai2 . . . AiN

• • ••• • ••• ••••

A | | | | | |

A A A A A (❨ (❨

Tensor networks

variational ansatz for QFT states based on entanglement properties

• ↑↓| i =X

ci1i2. . . iN |i1i2. . . iN i

matrix product states ci1i2. . . iN = Tr Ai1Ai2 . . . AiN

• • ••• • ••• ••••

A | | | | | |

A A A A A (❨ (❨

2 → 2 (rank Ai) N 2

Tensor networks

variational ansatz for QFT states based on entanglement properties

• ↑↓| i =X

ci1i2. . . iN |i1i2. . . iN i

matrix product states ci1i2. . . iN = Tr Ai1Ai2 . . . AiN

• • ••• • ••• ••••

A | | | | | |

A A A A A (❨ (❨

area law

2 → 2 (rank Ai) N 2

Tensor networks

variational ansatz for QFT states based on entanglement properties

• ↑↓| i =X

ci1i2. . . iN |i1i2. . . iN i

matrix product states ci1i2. . . iN = Tr Ai1Ai2 . . . AiN

• • ••• • ••• ••••

A | | | | | |

A A A A A (❨ (❨

area law

2 → 2 (rank Ai) N 2

Schwinger model ground state, low lying spectrum

(Pichler et al 2015; Buyens et al, 2014,2016)

(Banuls,Cichy,Jansen,Cirac, 2013; Rico et al, 2013)

real time simulations: Schwinger mechanism, quenches

Schwinger model quench massive Schwinger model + quench: turn on abruptly an electric field

(Buyens, Haegeman, van Acoleyen, Verschelde, Verstraete, 2014)

Schwinger model quench

pair production: energy density ~ fermion mass

massive Schwinger model + quench: turn on abruptly an electric field (Buyens, Haegeman, van Acoleyen, Verschelde, Verstraete, 2014)

Schwinger model quench

pair production: energy density ~ fermion mass

oscilations of electric field & particle number (out of phase)

small energies : revivals

(Buyens et al)

massive Schwinger model + quench: turn on abruptly an electric field (Buyens, Haegeman, van Acoleyen, Verschelde, Verstraete, 2014)

Schwinger model quench

pair production: energy density ~ fermion mass

oscilations of electric field & particle number (out of phase)

small energies : revivals

(Buyens et al)

massive Schwinger model + quench: turn on abruptly an electric field (Buyens, Haegeman, van Acoleyen, Verschelde, Verstraete, 2014)

oscilations of entanglement entropy

Schwinger model quench

pair production: energy density ~ fermion mass

small energy limit : perfect revivals

τ ≈ 2πΔm

Δm : mass of lowest stable excitation

oscilations of electric field & particle number (out of phase)

small energies : revivals

(Buyens et al)

massive Schwinger model + quench: turn on abruptly an electric field (Buyens, Haegeman, van Acoleyen, Verschelde, Verstraete, 2014)

oscilations of entanglement entropy

Schwinger model quench

pair production: energy density ~ fermion mass

small energy limit : perfect revivals

τ ≈ 2πΔm

Δm : mass of lowest stable excitation

|�i =X an

pn!

e�in�mt|ni

oscilations of electric field & particle number (out of phase)

small energies : revivals

(Buyens et al)

massive Schwinger model + quench: turn on abruptly an electric field (Buyens, Haegeman, van Acoleyen, Verschelde, Verstraete, 2014)

oscilations of entanglement entropy

On the holographic interpretation

holographic model: # fields >>1

Schwinger model: # fields ~1

On the holographic interpretation

BUT revivals depend on energy density

# fields

holographic model: # fields >>1

Schwinger model: # fields ~1

On the holographic interpretation

pairs of entangled quasiparticles

(Cardy,Calabrese, 2005)

stronger correlations when emitted at close points

entangled pairs stream away at c=1

xt=0

t

simple picture of massive to massless quench

BUT revivals depend on energy density

# fields

holographic model: # fields >>1

Schwinger model: # fields ~1

On the holographic interpretation

pairs of entangled quasiparticles

(Cardy,Calabrese, 2005)

stronger correlations when emitted at close points

entangled pairs stream away at c=1

xt=0

t

simple picture of massive to massless quench

l>2t

γ

l

BUT revivals depend on energy density

# fields

holographic model: # fields >>1

Schwinger model: # fields ~1

(Abajo,Aparicio Lopez, 2010;Balasubramanian et al, 2011)

On the holographic interpretation

pairs of entangled quasiparticles

(Cardy,Calabrese, 2005)

stronger correlations when emitted at close points

entangled pairs stream away at c=1

xt=0

t

simple picture of massive to massless quench

l>2t

γ

l

l

γ

l<2t

BUT revivals depend on energy density

# fields

holographic model: # fields >>1

Schwinger model: # fields ~1

(Abajo,Aparicio Lopez, 2010;Balasubramanian et al, 2011)

On the holographic interpretation

shell infall drift away of entangled excitations

pairs of entangled quasiparticles

(Cardy,Calabrese, 2005)

stronger correlations when emitted at close points

entangled pairs stream away at c=1

xt=0

t

simple picture of massive to massless quench

l>2t

γ

l

l

γ

l<2t

BUT revivals depend on energy density

# fields

holographic model: # fields >>1

Schwinger model: # fields ~1

(Abajo,Aparicio Lopez, 2010;Balasubramanian et al, 2011)

Comparing with AdS-HW

lowest excitation Δm → lowest normal mode

Comparing with AdS-HW

lowest excitation Δm → lowest normal mode

small energy quench maps to standing scalar pulse

Comparing with AdS-HW

lowest excitation Δm → lowest normal mode

small energy quench maps to standing scalar pulse

momentum zero coherent state

→ no radial displacement

Comparing with AdS-HW

lowest excitation Δm → lowest normal mode

small energy quench maps to standing scalar pulse

momentum zero coherent state

→ no radial displacement

~α ≈ 1

Comparing with AdS-HW

lowest excitation Δm → lowest normal mode

small energy quench maps to standing scalar pulse

momentum zero coherent state

→ no radial displacement

~α ≈ 1

electric field ↓

vev of O

Comparing with AdS-HW

lowest excitation Δm → lowest normal mode

small energy quench maps to standing scalar pulse

momentum zero coherent state

→ no radial displacement

~α ≈ 1

electric field ↓

vev of O

Comparing with AdS-HW

lowest excitation Δm → lowest normal mode

small energy quench maps to standing scalar pulse

momentum zero coherent state

→ no radial displacement

~α ≈ 1

2 4 6 8t

-6

-4

-2

2

4

6

XO\

α < 1 ~

electric field ↓

vev of O

Increasing the quench energy

resulting state should contain finite momentum modes

oscillating pulse must involve radial displacement

Increasing the quench energy

resulting state should contain finite momentum modes

oscillating pulse must involve radial displacement

check 1

ò

ô

0.0 0.2 0.4 0.6 0.8 1.0z

2

4

6

8

10r

e=0.28

e=0.7

α = .2~

Increasing the quench energy

resulting state should contain finite momentum modes

oscillating pulse must involve radial displacement

check 1

ò

ô

0.0 0.2 0.4 0.6 0.8 1.0z

2

4

6

8

10r

e=0.28

e=0.7

α = .2~

check 2 Φ=Φsol + ε lowest normal mode

Increasing the quench energy

resulting state should contain finite momentum modes

oscillating pulse must involve radial displacement

check 1

ò

ô

0.0 0.2 0.4 0.6 0.8 1.0z

2

4

6

8

10r

e=0.28

e=0.7

α = .2~radial localization increases with energy

e=0.5ô

ò

0.0 0.2 0.4 0.6 0.8 1.0z

2

4

6

8

10r

check 2 Φ=Φsol + ε lowest normal mode

The holographic dual of a quench

quench: sudden action abrupt time variation of boundary conditions

The holographic dual of a quench

quench: sudden action abrupt time variation of boundary conditions

varying bc at AdS3 boundary shell mass ∝ εδt

2

2 shell thickness ∝ δt

The holographic dual of a quench

quench: sudden action abrupt time variation of boundary conditions

varying bc at AdS3 boundary shell mass ∝ εδt

2

2 shell thickness ∝ δt

δt → 0 : singular configuration

(Buchel, Myers, van Niekerk, 2013;Das, Galante, Myers, 2014, 2015)

The holographic dual of a quench

quench: sudden action abrupt time variation of boundary conditions

varying bc at AdS3 boundary shell mass ∝ εδt

2

2 shell thickness ∝ δt

same for a wall variation of bc

δt → 0 : singular configuration

(Buchel, Myers, van Niekerk, 2013;Das, Galante, Myers, 2014, 2015)

The holographic dual of a quench

quench: sudden action abrupt time variation of boundary conditions

varying bc at AdS3 boundary shell mass ∝ εδt

2

2 shell thickness ∝ δt

finite energy quench → radial localization ~ energy

same for a wall variation of bc

δt → 0 : singular configuration

(Buchel, Myers, van Niekerk, 2013;Das, Galante, Myers, 2014, 2015)

The holographic dual of a quench

quench: sudden action abrupt time variation of boundary conditions

varying bc at AdS3 boundary shell mass ∝ εδt

2

2 shell thickness ∝ δt

finite energy quench → radial localization ~ energy

rising energy ~ increasing radial localization

same for a wall variation of bc

δt → 0 : singular configuration

(Buchel, Myers, van Niekerk, 2013;Das, Galante, Myers, 2014, 2015)

different dynamics of thin and broad shells

The holographic dual of a quench

quench: sudden action abrupt time variation of boundary conditions

varying bc at AdS3 boundary shell mass ∝ εδt

2

2 shell thickness ∝ δt

finite energy quench → radial localization ~ energy

revivals ~ standing waves rising energy ~ increasing radial localization

same for a wall variation of bc

δt → 0 : singular configuration

(Buchel, Myers, van Niekerk, 2013;Das, Galante, Myers, 2014, 2015)

different dynamics of thin and broad shells

“Typical” shell profileswhat bulk configurations can represent “typical” QFT out of equilibrium states?

“Typical” shell profileswhat bulk configurations can represent “typical” QFT out of equilibrium states?

no fine tuning involved↲

“Typical” shell profileswhat bulk configurations can represent “typical” QFT out of equilibrium states?

no fine tuning involved↲thin shells of small

mass are not typical

“Typical” shell profileswhat bulk configurations can represent “typical” QFT out of equilibrium states?

no fine tuning involved↲thin shells of small

mass are not typical

“Typical” shell profileswhat bulk configurations can represent “typical” QFT out of equilibrium states?

no fine tuning involved↲

able to resolve scales smaller than IR gap

thin shells of small mass are not typical

“Typical” shell profileswhat bulk configurations can represent “typical” QFT out of equilibrium states?

no fine tuning involved↲

able to resolve scales smaller than IR gap

energy density < gap

# fields2

thin shells of small mass are not typical

“Typical” shell profileswhat bulk configurations can represent “typical” QFT out of equilibrium states?

no fine tuning involved↲

able to resolve scales smaller than IR gap

energy density < gap

# fields2 not enough for Schwinger mechanism

virtual pairs can not separate further than ξ

thin shells of small mass are not typical

“Typical” shell profileswhat bulk configurations can represent “typical” QFT out of equilibrium states?

no fine tuning involved↲

able to resolve scales smaller than IR gap

energy density < gap

# fields2 not enough for Schwinger mechanism

virtual pairs can not separate further than ξ

thin shells of small mass are not typical

high energy

low energy

Conclusions

discuss general aspects of the holographic modeling of quenches using a simple setup

Conclusions

discuss general aspects of the holographic modeling of quenches using a simple setup

qualitative but detailed map between out of equilibrium QFT and the gravitational dynamics of collapsing shells

Conclusions

discuss general aspects of the holographic modeling of quenches using a simple setup

needed a further QFT understanding of small mass localized pulses

qualitative but detailed map between out of equilibrium QFT and the gravitational dynamics of collapsing shells

Conclusions

discuss general aspects of the holographic modeling of quenches using a simple setup

needed a further QFT understanding of small mass localized pulses

qualitative but detailed map between out of equilibrium QFT and the gravitational dynamics of collapsing shells

real time simulations have become recently accessible with tensor network techniques; holography provides a conceptually and perhaps also practical interesting alternative

Conclusions

discuss general aspects of the holographic modeling of quenches using a simple setup

needed a further QFT understanding of small mass localized pulses

qualitative but detailed map between out of equilibrium QFT and the gravitational dynamics of collapsing shells

real time simulations have become recently accessible with tensor network techniques; holography provides a conceptually and perhaps also practical interesting alternative

Thanks