Publications

Order by: publication date number of 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 | Toggle abstract · 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.

  32 citations

• Collision rate ansatz for quantum integrable systems

  Takato Yoshimura, Herbert Spohn

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

• Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54

  Katja Klobas, Bruno Bertini

  SciPost Phys. 11, 106 (2021) · published 20 December 2021 | Toggle abstract · pdf

  We study the out-of-equilibrium dynamics of the quantum cellular automaton Rule 54 using a time-channel approach. We exhibit a family of (non-equilibrium) product states for which we are able to describe exactly the full relaxation dynamics. We use this to prove that finite subsystems relax to a one-parameter family of Gibbs states. We also consider inhomogeneous quenches. Specifically, we show that when the two halves of the system are prepared in two different solvable states, finite subsystems at finite distance from the centre eventually relax to the non-equilibrium steady state (NESS) predicted by generalised hydrodynamics. To the best of our knowledge, this is the first exact description of the relaxation to a NESS in an interacting system and, therefore, the first independent confirmation of generalised hydrodynamics for an inhomogeneous quench.

  31 citations

• Free fermions at the edge of interacting systems

  Jean-Marie Stéphan

  SciPost Phys. 6, 057 (2019) · published 10 May 2019 | Toggle abstract · pdf

  We study the edge behavior of inhomogeneous one-dimensional quantum systems, such as Lieb-Liniger models in traps or spin chains in spatially varying magnetic fields. For free systems these fall into several universality classes, the most generic one being governed by the Tracy-Widom distribution. We investigate in this paper the effect of interactions. Using semiclassical arguments, we show that since the density vanishes to leading order, the strong interactions in the bulk are renormalized to zero at the edge, which simply explains the survival of Tracy-Widom scaling in general. For integrable systems, it is possible to push this argument further, and determine exactly the remaining length scale which controls the variance of the edge distribution. This analytical prediction is checked numerically, with excellent agreement. We also study numerically the edge scaling at fronts generated by quantum quenches, which provide new universality classes awaiting theoretical explanation.

  31 citations

• Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality

  Weicheng Ye, Meng Guo, Yin-Chen He, Chong Wang, Liujun Zou

  SciPost Phys. 13, 066 (2022) · published 26 September 2022 | Toggle abstract · pdf

  Lieb-Schultz-Mattis (LSM) theorems provide powerful constraints on the emergibility problem, i.e. whether a quantum phase or phase transition can emerge in a many-body system. We derive the topological partition functions that characterize the LSM constraints in spin systems with $G_s\times G_{int}$ symmetry, where $G_s$ is an arbitrary space group in one or two spatial dimensions, and $G_{int}$ is any internal symmetry whose projective representations are classified by $\mathbb{Z}_2^k$ with $k$ an integer. We then apply these results to study the emergibility of a class of exotic quantum critical states, including the well-known deconfined quantum critical point (DQCP), $U(1)$ Dirac spin liquid (DSL), and the recently proposed non-Lagrangian Stiefel liquid. These states can emerge as a consequence of the competition between a magnetic state and a non-magnetic state. We identify all possible realizations of these states on systems with $SO(3)\times \mathbb{Z}_2^T$ internal symmetry and either $p6m$ or $p4m$ lattice symmetry. Many interesting examples are discovered, including a DQCP adjacent to a ferromagnet, stable DSLs on square and honeycomb lattices, and a class of quantum critical spin-quadrupolar liquids of which the most relevant spinful fluctuations carry spin-$2$. In particular, there is a realization of spin-quadrupolar DSL that is beyond the usual parton construction. We further use our formalism to analyze the stability of these states under symmetry-breaking perturbations, such as spin-orbit coupling. As a concrete example, we find that a DSL can be stable in a recently proposed candidate material, NaYbO$_2$.

  30 citations

• Large fluctuations of the KPZ equation in a half-space

  Alexandre Krajenbrink, Pierre Le Doussal

  SciPost Phys. 5, 032 (2018) · published 12 October 2018 | Toggle abstract · pdf

  We investigate the short-time regime of the KPZ equation in $1+1$ dimensions and develop a unifying method to obtain the height distribution in this regime, valid whenever an exact solution exists in the form of a Fredholm Pfaffian or determinant. These include the droplet and stationary initial conditions in full space, previously obtained by a different method. The novel results concern the droplet initial condition in a half space for several Neumann boundary conditions: hard wall, symmetric, and critical. In all cases, the height probability distribution takes the large deviation form $P(H,t) \sim \exp( - \Phi(H)/\sqrt{t})$ for small time. We obtain the rate function $\Phi(H)$ analytically for the above cases. It has a Gaussian form in the center with asymmetric tails, $|H|^{5/2}$ on the negative side, and $H^{3/2}$ on the positive side. The amplitude of the left tail for the half-space is found to be half the one of the full space. As in the full space case, we find that these left tails remain valid at all times. In addition, we present here (i) a new Fredholm Pfaffian formula for the solution of the hard wall boundary condition and (ii) two Fredholm determinant representations for the solutions of the hard wall and the symmetric boundary respectively.

  28 citations

• Macroscopic fluctuation theory and current fluctuations in active lattice gases

  Tal Agranov, Sunghan Ro, Yariv Kafri, Vivien Lecomte

  SciPost Phys. 14, 045 (2023) · published 22 March 2023 | Toggle abstract · pdf

  We study the current large deviations for a lattice model of interacting active particles displaying a motility-induced phase separation (MIPS). To do this, we first derive the exact fluctuating hydrodynamics of the model in the large system limit. On top of the usual Gaussian noise terms the theory also presents Poissonian noise terms, that we fully account for. We find a dynamical phase transition between flat density profiles and sharply phase-separated traveling waves, and we derive the associated phase diagram together with the large deviation function for all phases, including the one displaying MIPS. We show how the results can be obtained using methods similar to those of equilibrium phase separation, in spite of the nonequilibrium nature of the problem.

  28 citations

• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum

  Caterina Zerba, Alessandro Silva

  SciPost Phys. Core 6, 051 (2023) · published 18 July 2023 | Toggle abstract · pdf

  We study dynamical phase transitions occurring in the stationary state of the dynamics of integrable many-body non-hermitian Hamiltonians, which can be either realized as a no-click limit of a stochastic Schrödinger equation or using spacetime duality of quantum circuits. In two specific models, the Transverse Field Ising Chain and the Long Range Kitaev Chain, we observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian: bounded entanglement entropy when the imaginary part of the quasi-particle spectrum is gapped and a logarithmic growth for gapless imaginary spectrum. This observation suggests the possibility to generalize the area-law theorem to non-Hermitian Hamiltonians.

  28 citations

• (Non) equilibrium dynamics: a (broken) symmetry of the Keldysh generating functional

  Camille Aron, Giulio Biroli, Leticia F. Cugliandolo

  SciPost Phys. 4, 008 (2018) · published 31 January 2018 | Toggle abstract · pdf

  We unveil the universal (model-independent) symmetry satisfied by Schwinger-Keldysh quantum field theories whenever they describe equilibrium dynamics. This is made possible by a generalization of the Schwinger-Keldysh path-integral formalism in which the physical time can be re-parametrized to arbitrary contours in the complex plane. Strong relations between correlation functions, such as the fluctuation-dissipation theorems, are derived as immediate consequences of this symmetry of equilibrium. In this view, quantum non-equilibrium dynamics -- e.g. when driving with a time-dependent potential -- are seen as symmetry-breaking processes. The symmetry-breaking terms of the action are identified as a measure of irreversibility, or entropy creation, defined at the level of a single quantum trajectory. Moreover, they are shown to obey quantum fluctuation theorems. These results extend stochastic thermodynamics to the quantum realm.

  27 citations

• Replica approach to the generalized Rosenzweig-Porter model

  Davide Venturelli, Leticia F. Cugliandolo, Grégory Schehr, Marco Tarzia

  SciPost Phys. 14, 110 (2023) · published 12 May 2023 | Toggle abstract · pdf

  The generalized Rosenzweig-Porter model with real (GOE) off-diagonal entries arguably constitutes the simplest random matrix ensemble displaying a phase with fractal eigenstates, which we characterize here by using replica methods. We first derive analytical expressions for the average spectral density in the limit in which the size $N$ of the matrix is large but finite. We then focus on the number of eigenvalues in a finite interval and compute its cumulant generating function as well as the level compressibility, i.e., the ratio of the first two cumulants: these are useful tools to describe the local level statistics. In particular, the level compressibility is shown to be described by a universal scaling function, which we compute explicitly, when the system is probed over scales of the order of the Thouless energy. Interestingly, the same scaling function is found to describe the level compressibility of the complex (GUE) Rosenzweig-Porter model in this regime. We confirm our results with numerical tests.

  27 citations