arXiv subjects

Tony Jin

Publications and source records attributed to Tony Jin.

At least 19 recordsLinked to original sources

arXiv2026

Nonlinear Fluctuating Hydrodynamics from Interacting Noisy Quantum Matter

A universal characterization of non-equilibrium steady states in interacting quantum many-body systems remains one of the central challenges of statistical physics. Here, we address this problem for a paradigmatic model of diffusive interacting quantum matter---the boundary-driven XXZ spin chain with bulk dephasing---and derive, directly from its microscopic Lindblad dynamics, an emergent classical Macroscopic Fluctuation Theory (MFT) governing its large-scale fluctuations. Crucially, the resulting hydrodynamics carries a density-dependent diffusivity and mobility as the fingerprint of interactions. This effective description enables the exact computation of the stationary density profile, long-range correlations, and the full counting statistics of the current, in excellent agreement with tensor-network simulations. Our work demonstrates that noisy quantum many-body systems can realize the universality class of genuinely interacting diffusive matter, beyond the constant-diffusivity class of the symmetric simple exclusion process, and establishes MFT as a powerful universal framework for interacting diffusive quantum systems.

cond-mat.stat-mech↗

arXiv2026

Symmetry as a route to generalized bosonic Kitaev chains

The bosonic Kitaev chain (BKC) model is a deceptively simple looking quadratic pairing Hamiltonian. Despite being purely Hermitian, it exhibits a number of striking non-Hermitian topological phenomena, including skin effects. We show here how symmetries play a key role in this model, and how identifying these allows one to develop generalized BKC-like models. We emphasize the surprising fact that any quadratic bosonic pairing Hamiltonian with a sublattice (chiral) symmetry necessarily has a dynamical matrix with an effective time reversal symmetry. This symmetry is unrelated to physical time-reversal, but enables non-trivial topological invariants. We also discuss how this symmetry is unrelated to another key property of the BKC, the decoupling of quadrature dynamics. This feature can instead be connected to a distinct symmetry, namely an effective particle-hole symmetry of the dynamical matrix. We discuss non-trivial generalized BKC models that only keep one of these two effective symmetries intact. We also provide a classification of all translationally-invariant 1D pairing Hamiltonians, and show connections between the BKC and a well-studied non-Hermitian fermionic system, the symplectic Hatano-Nelson model.

quant-ph↗

arXiv2026

Quantum-to-Classical Computability Transition via Negative Markov Chains

We develop a recently introduced representation of quantum dynamics based on sampling negative Markov chain processes. By introducing particles and antiparticles, this formalism maps generic quantum dynamics onto a Markov process defined over an exponentially large configuration space. Within this framework, quantum complexity arises from the proliferation of stochastic particles, which ultimately renders classical simulation and sampling intractable beyond a certain timescale. In the presence of noise, we demonstrate that for any unitary evolution generated by a linear combination of local or pairwise interactions, there exists at least one noise channel that effectively classicalizes the system by suppressing particle growth and making Monte Carlo sampling efficient. As a corollary, we show that for this class of unitaries, the dynamics of an open quantum spin chain subject to depolarizing noise undergoes an exact transition to classical simulability once the noise strength exceeds a critical threshold which can be efficiently determined for any model.

quant-ph↗

arXiv2026

Universal classical and quantum fluctuations in the large deviations of current of noisy quantum systems: The case of QSSEP and QSSIP

We study the fluctuation statistics of integrated currents in noisy quantum diffusive systems, focusing on the Quantum Symmetric Simple Exclusion and Inclusion Processes (QSSEP/QSSIP). These one-dimensional fermionic (QSSEP) and bosonic (QSSIP) models feature stochastic nearest-neighbor hopping driven by Brownian noise, together with boundary injection and removal processes. They provide solvable microscopic settings in which quantum coherence coexists with diffusion. Upon noise averaging, their dynamics reduce to those of the classical SSEP/SSIP. We show that the cumulant generating function of the integrated current, at large scales, obeys a large deviation principle. To leading order in system size and for each noise realization, it converges to that of the corresponding classical process, establishing a classical typicality of current fluctuations in these noisy quantum systems. We further demonstrate a direct connection with Macroscopic Fluctuation Theory (MFT), showing that the large-scale equations satisfied by biased quantum densities coincide with the steady-state Hamilton equations of MFT, thereby providing a microscopic quantum justification of the MFT framework in these models. Finally, we identify the leading finite-size corrections to the current statistics. We show the existence of subleading contributions of purely quantum origin, which are absent in the corresponding classical setting, and provide their explicit expressions for the second and third current cumulants. These quantum corrections are amenable to direct experimental or numerical verification, provided sufficient control over the noise realizations can be achieved. Their presence points toward the necessity of a quantum extension of Macroscopic Fluctuation Theory.

cond-mat.stat-mech↗

arXiv2025

Large deviations of density fluctuations in the boundary driven Quantum Symmetric Simple Inclusion Process

We consider the boundary driven Quantum Symmetric Simple Inclusion Process (QSSIP) which describes a one-dimensional system of bosonic particles with stochastic nearest-neighbor hopping, modeled as a Brownian motion, with gain/loss processes at the endpoints of the chain driving the system out-of-equilibrium. Although the averaged QSSIP dynamics differs from that of the Quantum Symmetric Simple Exclusion Process (QSSEP) - the analogous system where bosons are replaced by fermions - we show that, paradoxically, the dynamics of their matrices of two-point functions, along with all their fluctuations, coincide. In contrary, the underlying classical models differs significantly, as the bosonic statistics allow the inclusion of multiple particles at the same site, in contrast to (symmetric) simple exclusion processes (SSEP). We provide an exact derivation of the large deviation function of density fluctuations in QSSIP and, as a consequence, in the classical inclusion process (SSIP) by exploiting its quantum formulation. Remarkably, our study highlights that, both in QSSEP and QSSIP, fluctuations of the local densities are typically classical, i.e. the cumulant generating functions of the local densities are asymptotically self-averaging and converge toward those of the classical SSEP and SSIP, realization-wise. This provides a test of the conjectured almost sure classical behavior of transport fluctuations, at leading order in the system size, in noisy diffusive quantum many-body systems.

cond-mat.stat-mech↗

arXiv2025

Classical representation of the dynamics of quantum spin chains

Since the advent of quantum mechanics, classical probability interpretations have faced significant challenges. A notable issue arises with the emergence of negative probabilities when attempting to define the joint probability of non-commutative observables. In this work, we propose a resolution to this dilemma for quantum spin chains, by introducing an exact representation of their dynamics in terms of classical continuous-time Markov chains (CTMCs). These CTMCs effectively model the creation, annihilation, and propagation of pairs of classical particles and antiparticles. The quantum dynamics then emerges by averaging over various realizations of this classical process.

cond-mat.stat-mech↗

arXiv2024

QSSEP describes the fluctuations of quantum coherences in the Anderson model

Using the transfer matrix method, we numerically investigate the structure of spatial coherences and their fluctuations in the 3d Anderson model in the metallic phase when driven out-of-equilibrium by external leads at zero temperature and in linear response. We find that the stationary state entails non-local non-Gaussian correlations in the longitudinal direction, which are characteristic of diffusive non equilibrium steady states. These correlations are quantitatively matched, at least up to third order, by those analytically derived in the Quantum Symmetric Simple Exclusion Process (QSSEP) which describes diffusive fermions in 1d subject to dynamical disorder. Furthermore, the large deviation scaling and $U(1)$ invariance of these correlations imply a link between the Anderson model and free probability theory. Our findings suggest the existence of a universal structure of correlations in non-interacting diffusive quantum systems that might be captured by QSSEP.

cond-mat.stat-mech↗

arXiv2023

Measurement-induced phase transition in a single-body tight-binding model

We study the statistical properties of a single free quantum particle evolving coherently on a discrete lattice in ${\rm d}$ spatial dimensions where every lattice site is additionally subject to continuous measurement of the occupation number. Our numerical results indicate that the system undergoes a Measurement-induced Phase Transition (MiPT) for ${\rm d}>1$ from a $\textit{delocalized}$ to a $\textit{localized}$ phase as the measurement strength $\gamma$ is increased beyond a critical value $\gamma_{c}$. In the language of surface growth, the delocalized phase corresponds to a $\textit{smooth}$ phase while the localized phase corresponds to a $\textit{rough}$ phase. We support our numerical results with perturbative renormalization group (RG) computations which are in qualitative agreement at one-loop order.

quant-ph↗

arXiv2023

Entanglement phase transition due to reciprocity breaking without measurement or post-selection

Despite its fully unitary dynamics, the bosonic Kitaev chain (BKC) displays key hallmarks of non-Hermitian physics including non-reciprocal transport and the non-Hermitian skin effect. Here we demonstrate another remarkable phenomena: the existence of an entanglement phase transition (EPT) in a variant of the BKC that occurs as a function of a Hamiltonian parameter g, and which coincides with a transition from a reciprocal to a non-reciprocal phase. As g is reduced below a critical value, the post-quench entanglement entropy of a subsystem of size l goes from a volume-law phase where it scales as l to a super-volume law phase where it scales like lN with N the total system size. This EPT occurs for a system undergoing purely unitary evolution and does not involve measurements, post-selection, disorder or dissipation. We derive analytically the entanglement entropy out of and at the critical point for the $l=1$ and $l/N \ll 1$ case.

quant-ph↗

arXiv2023

Exact description of transport and non-reciprocity in monitored quantum devices

We study non-interacting fermionic systems undergoing continuous monitoring and driven by biased reservoirs. Averaging over the measurement outcomes, we derive exact formulas for the particle and heat flows in the system. We show that these currents feature competing elastic and inelastic components, which depend non-trivially on the monitoring strength $\gamma$. We highlight that monitor-induced inelastic processes lead to non-reciprocal currents, allowing to extract work from measurements without active feedback control. We illustrate our formalism with two distinct monitoring schemes providing measurement-induced power or cooling.~Optimal performances are found for values of the monitoring strength $\gamma$ which are hard to address with perturbative approaches.

quant-ph↗

arXiv2023

Bosonization of the interacting Su-Schrieffer-Heeger model

We derive the bosonization of the interacting fermionic Su-Schrieffer-Heeger (SSH) with open boundaries. We use the classical Euler-Lagrange equations of motions of the bosonized theory to compute the density profile of the Majorana edge mode and observe excellent agreement with numerical results, notably the localization of the mode near the boundaries. Remarkably, we find that repulsive or attractive interactions do not systematically localize or delocalize the edge mode but their effects depend on the value of the staggering parameter. We provide quantitative predictions of these effects on the localization length of the edge mode.

cond-mat.str-el↗

arXiv2022

Semi-classical theory of quantum stochastic resistors

We devise a semi-classical model to describe the transport properties of low-dimensional fermionic lattices under the influence of external quantum stochastic noise. These systems behave as quantum stochastic resistors, where the bulk particle transport is diffusive and obeys the Ohm/Fick's law. Here, we extend previous exact studies beyond the one-dimensional limit to ladder geometries and explore different dephasing mechanisms that are relevant to different physical systems, from solid-state to cold atoms. We find a non-trivial dependence of the conductance of these systems on the chemical potential of the reservoirs. We then introduce a semi-classical approach that is in good agreement with the exact numerical solution and provides an intuitive and simpler interpretation of transport in quantum stochastic resistors. Moreover, we find that the conductance of quantum ladders is insensitive to the coherence of the dephasing process along the direction transverse to transport, despite the fact that the system reaches different stationary states. We conclude by discussing the case of dissipative leads affected by dephasing, deriving the conditions for which they effectively behave as Markovian injectors of particles in the system.

cond-mat.stat-mech↗

arXiv2022

KPZ physics and phase transition in a classical single random walker under continuous measurement

We introduce and study a new model consisting of a single classical random walker undergoing continuous monitoring at rate $\gamma$ on a discrete lattice. Although such a continuous measurement cannot affect physical observables, it has a non-trivial effect on the probability distribution of the random walker. At small $\gamma$, we show analytically that the time-evolution of the latter can be mapped to the Stochastic Heat Equation (SHE). In this limit, the width of the log probability thus follows a Family-Vicsek scaling law, $N^{\alpha}f(t/N^{\alpha/\beta})$, with roughness and growth exponents corresponding to the Kardar-Parisi-Zhang (KPZ) universality class, i.e $\alpha^{\rm{1D}}_{\rm{KPZ}}=1/2$ and $\beta^{\rm{1D}}_{\rm{KPZ}}=1/3$ respectively. When $\gamma$ is increased outside this regime, we find numerically in 1D a crossover from the KPZ class to a new universality class characterized by exponents $\alpha^{1\rm{D}}_{\text{M}}\approx 1$ and $\beta^{1\rm{D}}_{\text{M}}\approx 1.4$. In 3D, varying $\gamma$ beyond a critical value $\gamma^c_{\rm{M}}$ leads to a phase transition from a smooth phase that we identify as the Edwards-Wilkinson (EW) class to a new universality class with $\alpha^{3\rm{D}}_{\text{M}}\approx1$.

cond-mat.stat-mech↗

arXiv2021

Exact description of quantum stochastic models as quantum resistors

We study the transport properties of generic out-of-equilibrium quantum systems connected to fermionic reservoirs. We develop a new method, based on an expansion of the current in terms of the inverse system size and out of equilibrium formulations such as the Keldysh technique and the Meir-Wingreen formula. Our method allows a simple and compact derivation of the current for a large class of systems showing diffusive/ohmic behavior. In addition, we obtain exact solutions for a large class of quantum stochastic Hamiltonians (QSHs) with time and space dependent noise, using a self consistent Born diagrammatic method in the Keldysh representation. We show that these QSHs exhibit diffusive regimes which are encoded in the Keldysh component of the single particle Green's function. The exact solution for these QSHs models confirms the validity of our system size expansion ansatz, and its efficiency in capturing the transport properties. We consider in particular three fermionic models: i) a model with local dephasing ii) the quantum simple symmetric exclusion process model iii) a model with long-range stochastic hopping. For i) and ii) we compute the full temperature and dephasing dependence of the conductance of the system, both for two- and four-points measurements. Our solution gives access to the regime of finite temperature of the reservoirs which could not be obtained by previous approaches. For iii), we unveil a novel ballistic-to-diffusive transition governed by the range and the nature (quantum or classical) of the hopping. As a by-product, our approach equally describes the mean behavior of quantum systems under continuous measurement.

cond-mat.stat-mech↗

arXiv2021

Interplay between transport and quantum coherences in free fermionic systems

We study the quench dynamics in free fermionic systems in the prototypical bipartitioning protocol obtained by joining two semi-infinite subsystems prepared in different states, aiming at understanding the interplay between quantum coherences in space in the initial state and transport properties. Our findings reveal that, under reasonable assumptions, the more correlated the initial state, the slower the transport is. Such statement is first discussed at qualitative level, and then made quantitative by introducing proper measures of correlations and transport ``speed''. Moreover, it is supported for fermions on a lattice by an exact solution starting from specific initial conditions, and in the continuous case by the explicit solution for a wider class of physically relevant initial states. In particular, for this class of states, we identify a function, that we dub \emph{transition map}, which takes the value of the stationary current as input and gives the value of correlation as output, in a protocol-independent way. As an aside technical result, in the discrete case, we give an expression of the full counting statistics in terms of a continuous kernel for a general correlated domain wall initial state, thus extending the recent results in [Moriya, Nagao and Sasamoto, JSTAT 2019(6):063105] on the one-dimensional XX spin chain.

quant-ph↗

arXiv2020

Generic transport formula for a system driven by Markovian reservoirs

We present a generic, compact formula for the current flowing in interacting and non-interacting systems which are driven out-of-equilibrium by biased reservoirs described by Lindblad jump operators. We show that, in the limit of high temperature and chemical potential, our formula is equivalent to the well-known Meir-Wingreen formula, which describes the current flowing through a system connected to fermionic baths, therefore bridging the gap between the two formalisms. Our formulation gives a systematic way to address the transport properties of correlated systems strongly driven out of equilibrium. As an illustration, we provide explicit calculations of the current in three cases : {\it i)} a single-site impurity {\it ii)} a free fermionic chain {\it iii)} a fermionic chain with loss/gain terms along the chain. In this last case, we find that the current across the system has the same behavior for loss or gain terms and depends on the loss/gain rate in a non-monotonic way.

quant-ph↗

arXiv2020

Solution to the Quantum Symmetric Simple Exclusion Process : the Continuous Case

The Quantum Symmetric Simple Exclusion Process (Q-SSEP) is a model for quantum stochastic dynamics of fermions hopping along the edges of a graph with Brownian noisy amplitudes and driven out-of-equilibrium by injection-extraction processes at a few vertices. We present a solution for the invariant probability measure of the one dimensional Q-SSEP in the infinite size limit by constructing the steady correlation functions of the system density matrix and quantum expectation values. These correlation functions code for a rich structure of fluctuating quantum correlations and coherences. Although our construction does not rely on the standard techniques from the theory of integrable systems, it is based on a remarkable interplay between the permutation groups and polynomials. We incidentally point out a possible combinatorial interpretation of the Q-SSEP correlation functions via a surprising connexion with geometric combinatorics and the associahedron polytopes.

math-ph↗

arXiv2020

Equilibration of quantum cat states

We study the equilibration properties of isolated ergodic quantum systems initially prepared in a cat state, i.e a macroscopic quantum superposition of states. Our main result consists in showing that, even though decoherence is at work in the mean, there exists a remnant of the initial quantum coherences visible in the strength of the fluctuations of the steady state. We back-up our analysis with numerical results obtained on the XXX spin chain with a random field along the z-axis in the ergodic regime and find good qualitative and quantitative agreement with the theory. We also present and discuss a framework where equilibrium quantities can be computed from general statistical ensembles without relying on microscopic details about the initial state, akin to the eigenstate thermalization hypothesis.

quant-ph↗