Quantum Quenches & Holography (with A Buchel, L Lehner & A - - PowerPoint PPT Presentation

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Quantum Quenches & Holography (with A Buchel, L Lehner & A - - PowerPoint PPT Presentation

Sep 14, 2022 399 likes •816 views

Quantum Quenches & Holography (with A Buchel, L Lehner & A van Niekerk; S Das & D Galante) Quantum Quenches: consider quantum system with Hamiltonian: prepare system in eigenstate of Hamiltonian abruptly turn on ;

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SLIDE 1

Quantum Quenches & Holography

(with A Buchel, L Lehner & A van Niekerk; S Das & D Galante)

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SLIDE 2

Quantum Quenches:

  • prepare system in eigenstate
  • f Hamiltonian
  • abruptly turn on ; system evolves unitarily according to
  • consider quantum system with Hamiltonian:
  • Question: How do observables, eg, expectation values and

correlation functions, evolve in time?

  • for most systems, coupling to environment is

unavoidable decoherence, dissipation

  • effects minimized for, eg, cold atoms in
  • ptical lattice

is there “universal” behaviour?

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SLIDE 3

Quantum Quenches & Holography:

  • theoretical progress made for variety systems: d=2 CFT,

(nearly) free fields, integrable models, . . . .

  • what can AdS/CFT correspondence offer?

strongly coupled field theories real-time analysis finite temperature (if desired) general spacetime dimension is there “universal” behaviour? what are organizing principles for out-of-equilibrium systems?

  • still seeking broadly applicable and efficient techniques
  • perhaps re-organization of problem will lead to new insights
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SLIDE 4

Chesler, Yaffe; Das, Nishioka, Takayanagi, Basu; Bhattacharyya, Minwalla; Abajo-Arrastia, Aparicio, Lopez; Albash, Johnson; Ebrahim, Headrick; Balasubramanian, Bernamonti, de Boer, Copland, Craps, Keski-Vakkuri, Mueller, Schafer, Shigemori, Staessens, Galli; Allias, Tonni; Keranen, Keski-Vakkuri, Thorlacius; Galante, Schvellinger; Carceres, Kundu; Wu; Garfinkle, Pando Zayas, Reichmann; Bhaseen, Gauntlett, Simons, Sonner, Wiseman; Auzzi, Elitzur, Gudnason, Rabinovici; . . . . . .

Quantum Quenches & Holography:

  • AdS/CFT lends itself to the study quantum quenches for a new

class of strongly coupled field theories

  • there has been a great deal of interest in the past few years
  • AdS/CFT connects far-from-equilibrium physics is naturally

leads to studying highly dynamical situations in gravity new dialogue with “numerical relativity”

  • much of work aimed at “thermalization” (eg, quark-gluon plasma)
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SLIDE 5

Quantum Quenches & Holography:

  • AdS/CFT allows us to study quantum quenches for strongly

coupled field theories in any number of dimensions Where are control parameters in AdS/CFT framework? gravity fields boundary operators AdS/CFT dictionary: eg, consider some scalar field in AdS: asymptotic solutions: equation of motion: integration constants become coupling and expectation value recall conformal dimension:

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Holographic Quantum Quench (cartoon):

  • asymp. AdS

boundary AdS geometry choice of b.c. launch scalar waves into AdS careful examination

  • f scalar tails

gravitational collapse produces black hole thermal state in boundary theory

  • quench thermal state, in expectation with previous analyses

Numerical Relativity

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SLIDE 7

Holographic Quantum Quench (cartoon):

  • asymp. AdS

boundary

  • “thermal quench”: quantum quench at finite temperature

AdS BH geometry choice of b.c. launch scalar waves into AdS careful examination

  • f scalar tails

gravitational collapse expands black hole thermal state in boundary theory

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SLIDE 8
  • determine “BH mass” with

diffeomorphism Ward identity*:

AdS BH geometry launch scalar waves into AdS gravitational collapse expands black hole

Holographic Thermal Quench:

  • choose conformal dimension,

and profile

  • solve linearized scalar eom

in fixed BH geometry determines integrate for , ie, * boundary constraint from Einstein eq’s

  • fix boundary dimension:
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SLIDE 9

Holographic Thermal Quench:

  • profile:
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Holographic Thermal Quench:

  • lessons learned:
  • bdry theory has new divergences: ( = UV cut-off scale)
  • holography gives well-defined approach to renormalize bdry QFT
  • 1. Renormalization of (strongly coupled) boundary QFT with

time-dependent couplings works in a straightforward way

  • familiar in the context of QFT in curved backgrounds
  • new log divergences lead to new scheme dependent ambiguities

(Bianchi, Freedman & Skenderis; Aharony, Buchel & Yarom; Petkou & Skenderis; Emparan, Johnson & Myers; . . . )

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SLIDE 11

Holographic Thermal Quench:

  • profile:
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Holographic Thermal Quench:

  • lessons learned:
  • 2. Response to “fast” quenches exhibits universal scaling
  • for example:

yields physical divergence!!

  • seems to indicate instantaneous quench is problematic

with , get abrupt jump in

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SLIDE 13

Holographic Thermal Quench:

  • lessons learned:
  • 2. Response to “fast” quenches exhibits universal scaling
  • for example:

yields physical divergence!!

  • seems to indicate instantaneous quench is problematic
  • compare to seminal work of, eg, Calabrese & Cardy

“instantaneous quench” is basic starting point ► identified a physical problem? ► simply an issue with perturbative expansion?

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Holographic Quantum Quench (cartoon):

AdS geometry gravitational collapse produces black hole

Question: What is ?

  • nly consider

this region

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SLIDE 15

Holographic Quantum Quench (cartoon):

AdS geometry gravitational collapse produces black hole

Question: What is ?

  • nly consider

this region

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SLIDE 16

Holographic Quantum Quench (cartoon):

AdS geometry gravitational collapse produces black hole

Question: What is ?

  • nly consider

this region

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SLIDE 17

Generalizing “Fast” Quenches:

Question: What is ?

  • as we scale , only “tiny” region of solution in asymptotic

AdS relevant for this question certainly full numerical simulations are not needed solvable with purely analytic approach!!

  • focus: full details of evolution, eg, approach to final state, are not

determined but allows us to understand scaling behaviour

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Generalizing “Fast” Quenches:

Question: What is ?

  • solve full bulk equations of motion perturbatively for
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SLIDE 19

Generalizing “Fast” Quenches:

recall and

  • key: asymptotic fields in AdS decay in precise manner (ie,

Fefferman-Graham expansion) nonlinearities unimportant! linear scalar eq:

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Generalizing “Fast” Quenches:

  • set and take limit (while kept fixed)

natural to scale coordinates: eg,

nonlinearities in eom

  • key: asymptotic fields in AdS decay in precise manner (ie,

Fefferman-Graham expansion) nonlinearities unimportant!

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  • key: asymptotic fields in AdS decay in precise manner (ie,

Fefferman-Graham expansion) nonlinearities unimportant!

Generalizing “Fast” Quenches:

  • set and take limit (while kept fixed)

natural to scale coordinates: add: “matching bc”:

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Generalizing “Fast” Quenches:

  • set and take limit (while kept fixed)

natural to scale coordinates: need:

  • relevant solution = linearized scalar solution in AdS space!
  • similar scaling arguments yield:
  • key: asymptotic fields in AdS decay in precise manner (ie,

Fefferman-Graham expansion) nonlinearities unimportant! but solving for full nonlinear problem!

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Generalizing “Fast” Quenches:

  • analytic solutions, eg:

0.2 0.4 0.6 0.8 1.0 at 0.2 0.4 0.6 0.8 1.0 ap0

0.2 0.4 0.6 0.8 1.0 40 20 20 40 ap2

where

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► identified a physical problem?

  • as we scale , only “tiny” region in asymptotic AdS relevant

Generalizing “Fast” Quenches:

  • relevant solution = linearized scalar solution in AdS space!
  • general scaling with holographic dictionary,

ie, “energy conservation”:

  • matches previous perturbative numerical calc’s (for d=4)
  • result here applies for full nonlinear solution!!

► simply an issue with perturbative expansion? effect

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SLIDE 25
  • operators in range seem to be okay

Generalizing “Fast” Quenches:

  • yields physical divergence for

“instantaneous” quench seems problematic!?!

  • can consider various scaling limits:

as finite but divergent as finite but vanishes but would not be “standard” protocol

  • note UV fixed point, ie, CFT, is source of divergence
  • strongly coupled holographic QFT versus free fields???
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Generalizing “Fast” Quenches:

  • compare directly to C&C, ie, quench mass of a free scalar:
  • quench with finite and examine limit
  • eq. of motion:
  • example in: Birrell & Davies, “Quantum Fields in Curved Space”

eg, “in” modes:

with

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SLIDE 27

Generalizing “Fast” Quenches:

  • compare directly to C&C, ie, quench mass of a free scalar:
  • given individual modes, consider two point correlator
  • yields simple result in the limit :

recover the “sudden quench” results of C&C!!

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SLIDE 28

Generalizing “Fast” Quenches:

  • consider response:
  • UV divergences: eg, consider a constant mass
  • regulated response (d=5):

where

  • following holographic example, UV divergences are removed by

adding appropriate counterterms in effective action

  • “wherever you see terms with , subtract them off”
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SLIDE 29

Generalizing “Fast” Quenches:

  • regulated response (d=5):

4 2 2 4 6 8 10 0.5 0.0 0.5 1.0 1.5 ΡΗ

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SLIDE 30

10 100 50 20 200 30 15 150 70 104 0.1 100 105 108 1011

Generalizing “Fast” Quenches:

  • regulated response (d=5):

slope: compare holographic scaling:

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SLIDE 31

10 100 50 20 200 30 15 150 70 104 0.1 100 105 108 1011

Generalizing “Fast” Quenches:

  • regulated response (d=9,8,7,6,5,4):

holographic scaling reproduced by free field!

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SLIDE 32

Generalizing “Fast” Quenches:

  • can verify that Ward identity is satisified:
  • evaluate independently and compare above numerically
  • some analytic progress: expand for small , find

(odd d)

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Generalizing “Fast” Quenches:

  • extend free field calculations to fermions:
  • quench with finite and examine limit
  • eq. of motion:
  • again, related to problem of fermions in a cosmological bkgd
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10 100 50 20 200 30 15 150 70 1 100 104 106 108 1010

Generalizing “Fast” Quenches:

  • regulated response (d=7,6,5,4,3,2):

holographic scaling reproduced by free field!

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Generalizing “Fast” Quenches:

why is holographic scaling reproduced by free field?!?!?

  • consider

with

  • apply conformal perturbation theory
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Generalizing “Fast” Quenches:

why is holographic scaling reproduced by free field?!?!?

  • consider

with

  • apply conformal perturbation theory
  • organized with dimensionless effective coupling:
  • in limit fixed and : !!

leading term dominates:

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SLIDE 37

Generalizing “Fast” Quenches:

  • for example:
  • holographic scaling should appear quite generally!!
  • what about sudden quenches of C&C??
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SLIDE 38

10 100 50 20 200 30 15 150 70 104 0.1 100 105 108 1011

Generalizing “Fast” Quenches:

  • regulated response (d=9,8,7,6,5,4,3):

holographic scaling reproduced by free field!

0, -1

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SLIDE 39

10 100 50 20 200 30 15 150 70 104 0.1 100 105 108 1011

Generalizing “Fast” Quenches:

  • regulated response (d=9,8,7,6,5,4,3):

scaling need not produce divergence much of C&C is d=2,3

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SLIDE 40

Generalizing “Fast” Quenches:

  • for example:
  • holographic scaling should appear quite generally!!
  • what about sudden quenches of C&C??

suggests ???

  • an order of limits???
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SLIDE 41
  • quantum quenches: interesting arena for holographic study

Lots to explore!

Conclusions: ► both lessons 1 & 2 apply beyond holographic arena!! ► much of fast holographic quenches analytically accessible

  • 1. Renormalization of (strongly coupled) boundary QFT with

time-dependent couplings works in a straightforward way

  • lessons learned:
  • 2. Response to fast quenches exhibits universal scaling