Diffusive Heat Waves in Random Conformal Field Theory

Langmann, Edwin; Moosavi, Per

doi:10.1103/physrevlett.122.020201

Cited by 34 publications

(55 citation statements)

References 32 publications

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“…The problem we will treat is the one of a gas of hard-core bosons, also known as the Tonks-Girardeau gas, in a time-dependent harmonic potential V (x, t). This problem is well-known to be exactly solvable [34][35][36], and our goal is to use it to illustrate our approach, which extends recent works by others and by ourselves and our collaborators [1,[37][38][39][40][41][42][43][44][45][46][47][48][49][50][51]. We will see that we recover some known results about equal-time correlations, and we uncover new ones, including results for correlation functions at different time.…”

Section: Contextsupporting

confidence: 57%

“…Refs. [1,[37][38][39][40][41][42][43][44][45][46][47][48][49][50][51]), by considering a truly dynamical situation: a breathing gas of hard core bosons at zero temperature. In particular, we have found new formulas for the 1/N ∼ ħ h → 0 asymptotics of 2n-point functions of boson creation/annihilation operators, and also for fermionic observables for which we provided numerical checks.…”

Section: Resultsmentioning

confidence: 99%

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Conformal field theory on top of a breathing one-dimensional gas of hard core bosons

2019

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The recent results of [J. Dubail, J.-M. Stéphan, J. Viti, P. Calabrese, Scipost Phys. 2, 002 (2017)], which aim at providing access to large scale correlation functions of inhomogeneous critical one-dimensional quantum systems —e.g. a gas of hard core bosons in a trapping potential— are extended to a dynamical situation: a breathing gas in a time-dependent harmonic trap. Hard core bosons in a time-dependent harmonic potential are well known to be exactly solvable, and can thus be used as a benchmark for the approach. An extensive discussion of the approach and of its relation with classical and quantum hydrodynamics in one dimension is given, and new formulas for correlation functions, not easily obtainable by other methods, are derived. In particular, a remarkable formula for the large scale asymptotics of the bosonic \boldsymbol{n}𝐧-particle function \boldsymbol{\left< \Psi^\dagger (x_1,t_1) \dots \Psi^\dagger (x_n,t_n) \Psi(x_1',t_1') \dots \Psi(x_n',t_n') \right>} is obtained. Numerical checks of the approach are carried out for the fermionic two-point function —easier to access numerically in the microscopic model than the bosonic one— with perfect agreement.

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Section: Contextsupporting

confidence: 57%

Section: Resultsmentioning

confidence: 99%

Conformal field theory on top of a breathing one-dimensional gas of hard core bosons

2019

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“…One framework amenable to exact analytical solutions is given by conformal field theory (CFT) in 1 + 1 dimensions. Here, we focus on the recent concept of inhomogeneous CFT, whose applications include effective descriptions of trapped ultracold atoms, inhomogeneous gapless spins chains, and quantum fluctuations in generalized hydrodynamics [24][25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

“…Here, H 1 and H 2 are given by any smooth deformation of standard Minkowskian CFT on the cylinder R × [−L/2, L/2]. We refer to the above general smoothly deformed CFT as inhomogeneous CFT [27][28][29]. They are defined by…”

Section: Introductionmentioning

confidence: 99%

Geometric approach to inhomogeneous Floquet systems

Lapierre

Moosavi

2021

Phys. Rev. B

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We present a new geometric approach to Floquet many-body systems described by inhomogeneous conformal field theory in 1+1 dimensions. It is based on an exact correspondence with dynamical systems on the circle that we establish and use to prove existence of (non)heating phases characterized by the (absence) presence of fixed or higher-periodic points of coordinate transformations encoding the time evolution: Heating corresponds to energy and excitations concentrating exponentially fast at unstable such points while nonheating to pseudoperiodic motion. We show that the heating rate (serving as the order parameter for transitions between these two) can have cusps, even within the overall heating phase, and that there is a rich structure of phase diagrams with different heating phases distinguishable through kinks in the entanglement entropy, reminiscent of Lifshitz phase transitions. Our geometric approach generalizes previous results for a subfamily of similar systems that used only the sl(2) algebra to general smooth deformations that require the full infinite-dimensional Virasoro algebra, and we argue that it has wider applicability, even beyond conformal field theory.

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“…This curved CFT approach has already been employed for many applications: the entanglement entropies [40], the entanglement hamiltonian [41], and some correlation functions [40,42] have been calculated for many different situations in inhomogeneous freefermion models; the field theory description of the rainbow model was also unveiled [43], spin chains with gradients were studied [44], and the presence of curved lightcones has been investigated [45]. All these applications refer to free models, but some results for interacting systems are also available [46][47][48][49]. The goal of this work is to understand whether and in which form the universality features of the entanglement in low-lying excited states persist in inhomogeneous settings, as a Figure 1.…”

Section: Introductionmentioning

confidence: 99%

Entanglement and relative entropies for low-lying excited states in inhomogeneous one-dimensional quantum systems

2019

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Conformal field theories in curved backgrounds have been used to describe inhomogeneous one-dimensional systems, such as quantum gases in trapping potentials and non-equilibrium spin chains. This approach provided, in a elegant and simple fashion, non-trivial analytic predictions for quantities, such as the entanglement entropy, that are not accessible through other methods. Here, we generalise this approach to low-lying excited states, focusing on the entanglement and relative entropies in an inhomogeneous free-fermionic system. Our most important finding is that the universal scaling function characterising these entanglement measurements is the same as the one for homogeneous systems, but expressed in terms of a different variable. This new scaling variable is a nontrivial function of the subsystem length and system's inhomogeneity that is easily written in terms of the curved metric. We test our predictions against exact numerical calculations in the free Fermi gas trapped by a harmonic potential, finding perfect agreement. arXiv:1810.02287v1 [cond-mat.stat-mech]

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Diffusive Heat Waves in Random Conformal Field Theory

Cited by 34 publications

References 32 publications

Conformal field theory on top of a breathing one-dimensional gas of hard core bosons

Conformal field theory on top of a breathing one-dimensional gas of hard core bosons

Geometric approach to inhomogeneous Floquet systems

Entanglement and relative entropies for low-lying excited states in inhomogeneous one-dimensional quantum systems

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