Publications

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Non-unitary dynamics of Sachdev-Ye-Kitaev chain

Chunxiao Liu, Pengfei Zhang, Xiao Chen

SciPost Phys. 10, 048 (2021) · published 23 February 2021 | · pdf

We construct a series of one-dimensional non-unitary dynamics consisting of both unitary and imaginary evolutions based on the Sachdev-Ye-Kitaev model. Starting from a short-range entangled state, we analyze the entanglement dynamics using the path integral formalism in the large $N$ limit. Among all the results that we obtain, two of them are particularly interesting: (1) By varying the strength of the imaginary evolution, the interacting model exhibits a first order phase transition from the highly entangled volume law phase to an area law phase; (2) The one-dimensional free fermion model displays an extensive critical regime with emergent two-dimensional conformal symmetry.

34 citations
Entanglement dynamics in Rule 54: Exact results and quasiparticle picture

Katja Klobas, Bruno Bertini

SciPost Phys. 11, 107 (2021) · published 20 December 2021 | · pdf

We study the entanglement dynamics generated by quantum quenches in the quantum cellular automaton Rule 54. We consider the evolution from a recently introduced class of solvable initial states. States in this class relax (locally) to a one-parameter family of Gibbs states and the thermalisation dynamics of local observables can be characterised exactly by means of an evolution in space. Here we show that the latter approach also gives access to the entanglement dynamics and derive exact formulas describing the asymptotic linear growth of all Rényi entropies in the thermodynamic limit and their eventual saturation for finite subsystems. While in the case of von Neumann entropy we recover exactly the predictions of the quasiparticle picture, we find no physically meaningful quasiparticle description for other Rényi entropies. Our results apply to both homogeneous and inhomogeneous quenches.

33 citations
Subsystem Rényi entropy of thermal ensembles for SYK-like models

Pengfei Zhang, Chunxiao Liu, Xiao Chen

SciPost Phys. 8, 094 (2020) · published 26 June 2020 | · pdf

The Sachdev-Ye-Kitaev model is an $N$ -modes fermionic model with infinite range random interactions. In this work, we study the thermal R\'enyi entropy for a subsystem of the SYK model using the path-integral formalism in the large- $N$ limit. The results are consistent with exact diagonalization [1] and can be well approximated by thermal entropy with an effective temperature [2] when subsystem size $M\leq N/2$ . We also consider generalizations of the SYK model with quadratic random hopping term or $U(1)$ charge conservation.

33 citations
Quench dynamics of the Ising field theory in a magnetic field

Kristóf Hódsági, Márton Kormos, Gábor Takács

SciPost Phys. 5, 027 (2018) · published 25 September 2018 | · pdf

We numerically simulate the time evolution of the Ising field theory after quenches starting from the $E_8$ integrable model using the Truncated Conformal Space Approach. The results are compared with two different analytic predictions based on form factor expansions in the pre-quench and post-quench basis, respectively. Our results clarify the domain of validity of these expansions and suggest directions for further improvement. We show for quenches in the $E_8$ model that the initial state is not of the integrable pair state form. We also construct quench overlap functions and show that their high-energy asymptotics are markedly different from those constructed before in the sinh/sine-Gordon theory, and argue that this is related to properties of the ultraviolet fixed point.

33 citations
Fast counting with tensor networks

Stefanos Kourtis, Claudio Chamon, Eduardo R. Mucciolo, Andrei E. Ruckenstein

SciPost Phys. 7, 060 (2019) · published 12 November 2019 | · pdf

We introduce tensor network contraction algorithms for counting satisfying assignments of constraint satisfaction problems (#CSPs). We represent each arbitrary #CSP formula as a tensor network, whose full contraction yields the number of satisfying assignments of that formula, and use graph theoretical methods to determine favorable orders of contraction. We employ our heuristics for the solution of #P-hard counting boolean satisfiability (#SAT) problems, namely monotone #1-in-3SAT and #Cubic-Vertex-Cover, and find that they outperform state-of-the-art solvers by a significant margin.

32 citations
Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point

Grégoire Misguich, Nicolas Pavloff, Vincent Pasquier

SciPost Phys. 7, 025 (2019) · published 29 August 2019 | · pdf

We study the dynamics of a spin-1/2 XXZ chain which is initially prepared in a domain-wall state. We compare the results of time-dependent Density Matrix Renormalization Group simulations with those of an effective description in terms of a classical anisotropic Landau-Lifshitz (LL) equation. Numerous quantities are analyzed: magnetization (x, y and z components), energy density, energy current, but also some spin-spin correlation functions or entanglement entropy in the quantum chain. Without any adjustable parameter a quantitative agreement is observed between the quantum and the LL problems in the long time limit, when the models are close to the isotropic point. This is explained as a consequence of energy conservation. At the isotropic point the mapping between the LL equation and the nonlinear Schr\"odinger equation is used to construct a variational solution capturing several aspects of the problem.

31 citations
A localization transition underlies the mode-coupling crossover of glasses

Daniele Coslovich, Andrea Ninarello, Ludovic Berthier

SciPost Phys. 7, 077 (2019) · published 6 December 2019 | · pdf

We study the equilibrium statistical properties of the potential energy landscape of several glass models in a temperature regime so far inaccessible to computer simulations. We show that unstable modes of the stationary points undergo a localization transition in real space close to the mode-coupling crossover temperature determined from the dynamics. The concentration of localized unstable modes found at low temperature is a non-universal, finite dimensional feature not captured by mean-field glass theory. Our analysis reconciles, and considerably expands, previous conflicting numerical results and provides a characteristic temperature for glassy dynamics that unambiguously locates the mode-coupling crossover.

31 citations
Collision rate ansatz for quantum integrable systems

Takato Yoshimura, Herbert Spohn

SciPost Phys. 9, 040 (2020) · published 15 September 2020 | · pdf

For quantum integrable systems the currents averaged with respect to a generalized Gibbs ensemble are revisited. An exact formula is known, which we call “collision rate ansatz”.While there is considerable work to confirm this ansatz in various models, our approach uses the symmetry of the current-charge susceptibility matrix, which holds in great generality. Besides some technical assumptions, the main input is the availability of a self-conserved current, i.e. some current which is itself conserved. The collision rate ansatz is then derived. The argument is carried out in detail for the Lieb-Liniger model and the Heisenberg XXZ chain. The Fermi-Hubbard is not covered, since no self-conserved current seems to exist. It is also explained how from the existence of a boost operator a self-conserved current can be deduced.

31 citations
Navigator function for the conformal bootstrap

Marten Reehorst, Slava Rychkov, David Simmons-Duffin, Benoit Sirois, Ning Su, Balt van Rees

SciPost Phys. 11, 072 (2021) · published 28 September 2021 | · pdf

Current numerical conformal bootstrap techniques carve out islands in theory space by repeatedly checking whether points are allowed or excluded. We propose a new method for searching theory space that replaces the binary information “allowed”/“excluded” with a continuous “navigator” function that is negative in the allowed region and positive in the excluded region. Such a navigator function allows one to efficiently explore high-dimensional parameter spaces and smoothly sail towards any islands they may contain. The specific functions we introduce have several attractive features: they are well-defined in large regions of parameter space, can be computed with standard methods, and evaluation of their gradient is immediate due to an SDP gradient formula that we provide. The latter property allows for the use of efficient quasi-Newton optimization methods, which we illustrate by navigating towards the 3d Ising island.

31 citations
Integrable matrix models in discrete space-time

Žiga Krajnik, Enej Ilievski, Tomaž Prosen

SciPost Phys. 9, 038 (2020) · published 14 September 2020 | · pdf

We introduce a class of integrable dynamical systems of interacting classical matrix-valued fields propagating on a discrete space-time lattice, realized as many-body circuits built from elementary symplectic two-body maps. The models provide an efficient integrable Trotterization of non-relativistic $\sigma$ -models with complex Grassmannian manifolds as target spaces, including, as special cases, the higher-rank analogues of the Landau-Lifshitz field theory on complex projective spaces. As an application, we study transport of Noether charges in canonical local equilibrium states. We find a clear signature of superdiffusive behavior in the Kardar-Parisi-Zhang universality class, irrespectively of the chosen underlying global unitary symmetry group and the quotient structure of the compact phase space, providing a strong indication of superuniversal physics.

31 citations

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