arXiv subjects

Jerome Dubail

Publications and source records attributed to Jerome Dubail.

17 recordsLinked to original sources

arXiv2026

Exact Results for the Symmetric Dyson Exclusion Process

The symmetric Dyson exclusion process (SDEP) is an exclusion process on the lattice with a long-range logarithmic Coulomb-type interaction. It appears in several equivalent forms: as symmetric random walkers conditioned, in the Doob-transform sense, not to collide; as the maximal-activity limit of a conditioned SSEP; and as a ground-state transform of the spin- 1/2 XX chain. In this work, we exploit this latter representation to obtain exact evolution formulas from deterministic initial configurations. The resulting determinantal kernel is expressed through a finite interpolation expression in terms of Lagrange polynomials, leading to explicit density evolution in finite and infinite lattices. For the melting of a densely packed block, we show that the full hierarchy of density moments is governed by a finite-dimensional polynomial algebra, and we identify Catalan numbers in the leading time coefficients. We also derive the Euler-scale density profile and the arctic curve separating frozen and liquid regions, and show that they coincide with conjectured hydrodynamic results obtained in a previous work.

cond-mat.stat-mech↗

arXiv2025

Emergent Hydrodynamics in an Exclusion Process with Long-Range Interactions

We study the symmetric Dyson exclusion process (SDEP) - a lattice gas with exclusion and long-range, Coulomb-type interactions that emerge both as the maximal-activity limit of the symmetric exclusion process and as a discrete version of Dyson's Brownian motion on the unitary group. Exploiting an exact ground-state (Doob) transform, we map the stochastic generator of the SDEP onto the spin-$1/2$ XX quantum chain, which in turn admits a free-fermion representation. At macroscopic scales we conjecture that the SDEP displays ballistic (Eulerian) scaling and non-local hydrodynamics governed by the equation $\partial_t \rho+\partial_x j[\rho]=0$ with $j[\rho]=(1/\pi)\sin(\pi\rho(x,t))\sinh(\pi\mathcal{H}\rho(x,t))$, where $\mathcal{H}$ is the Hilbert transform, making the current a genuinely non-local functional of the density. This non-local one-field description is equivalent to a local two-field "complex Hopf" system for finite particle density. Closed evolution formulas allow us to solve the melting of single and double block initial states, producing limit shapes and arctic curves that agree with large-scale Monte Carlo simulations. The model thus offers a tractable example of emergent non-local hydrodynamics driven by long-range interactions.

cond-mat.stat-mech↗

arXiv2024

Entanglement asymmetry in CFT and its relation to non-topological defects

The entanglement asymmetry is an information based observable that quantifies the degree of symmetry breaking in a region of an extended quantum system. We investigate this measure in the ground state of one dimensional critical systems described by a CFT. Employing the correspondence between global symmetries and defects, the analysis of the entanglement asymmetry can be formulated in terms of partition functions on Riemann surfaces with multiple non-topological defect lines inserted at their branch cuts. For large subsystems, these partition functions are determined by the scaling dimension of the defects. This leads to our first main observation: at criticality, the entanglement asymmetry acquires a subleading contribution scaling as $\log \ell / \ell$ for large subsystem length $\ell$. Then, as an illustrative example, we consider the XY spin chain, which has a critical line described by the massless Majorana fermion theory and explicitly breaks the $U(1)$ symmetry associated with rotations about the $z$-axis. In this situation the corresponding defect is marginal. Leveraging conformal invariance, we relate the scaling dimension of these defects to the ground state energy of the massless Majorana fermion on a circle with equally-spaced point defects. We exploit this mapping to derive our second main result: the exact expression for the scaling dimension associated with $n$ of defects of arbitrary strengths. Our result generalizes a known formula for the $n=1$ case derived in several previous works. We then use this exact scaling dimension to derive our third main result: the exact prefactor of the $\log \ell/\ell$ term in the asymmetry of the critical XY chain.

hep-th↗

arXiv2022

Rise and fall, and slow rise again, of operator entanglement under dephasing

The operator space entanglement entropy, or simply 'operator entanglement' (OE), is an indicator of the complexity of quantum operators and of their approximability by Matrix Product Operators (MPO). We study the OE of the density matrix of 1D many-body models undergoing dissipative evolution. It is expected that, after an initial linear growth reminiscent of unitary quench dynamics, the OE should be suppressed by dissipative processes as the system evolves to a simple stationary state. Surprisingly, we find that this scenario breaks down for one of the most fundamental dissipative mechanisms: dephasing. Under dephasing, after the initial 'rise and fall' the OE can rise again, increasing logarithmically at long times. Using a combination of MPO simulations for chains of infinite length and analytical arguments valid for strong dephasing, we demonstrate that this growth is inherent to a $U(1)$ conservation law. We argue that in an XXZ spin-model and a Bose-Hubbard model the OE grows universally as $\frac{1}{4} \log_2 t$ at long times, and as $\frac{1}{2} \log_2 t$ for a Fermi-Hubbard model. We trace this behavior back to anomalous classical diffusion processes.

quant-ph↗

arXiv2020

The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas

We theoretically investigate the effects of atom losses in the one-dimensional (1D) Bose gas with repulsive contact interactions, a famous quantum integrable system also known as the Lieb-Liniger gas. The generic case of K-body losses (K = 1,2,3,...) is considered. We assume that the loss rate is much smaller than the rate of intrinsic relaxation of the system, so that at any time the state of the system is captured by its rapidity distribution (or, equivalently, by a Generalized Gibbs Ensemble). We give the equation governing the time evolution of the rapidity distribution and we propose a general numerical procedure to solve it. In the asymptotic regimes of vanishing repulsion -- where the gas behaves like an ideal Bose gas -- and hard-core repulsion -- where the gas is mapped to a non-interacting Fermi gas -- we derive analytic formulas. In the latter case, our analytic result shows that losses affect the rapidity distribution in a non-trivial way, the time derivative of the rapidity distribution being both non-linear and non-local in rapidity space.

cond-mat.quant-gas↗

arXiv2020

Generalized hydrodynamics in strongly interacting 1D Bose gases

The dynamics of strongly interacting many-body quantum systems are notoriously complex and difficult to simulate. A new theory, generalized hydrodynamics (GHD), promises to efficiently accomplish such simulations for nearly-integrable systems. It predicts the evolution of the distribution of rapidities, which are the momenta of the quasiparticles in integrable systems. GHD was recently tested experimentally for weakly interacting atoms, but its applicability to strongly interacting systems has not been experimentally established. Here we test GHD with bundles of one-dimensional (1D) Bose gases by performing large trap quenches in both the strong and intermediate coupling regimes. We measure the evolving distribution of rapidities, and find that theory and experiment agree well over dozens of trap oscillations, for average dimensionless coupling strengths that range from 0.3 to 9.3. By also measuring momentum distributions, we gain experimental access to the interaction energy and thus to how the quasiparticles themselves evolve. The accuracy of GHD demonstrated here confirms its wide applicability to the simulation of nearly-integrable quantum dynamical systems. Future experimental studies are needed to explore GHD in spin chains, as well as the crossover between GHD and regular hydrodynamics in the presence of stronger integrability breaking perturbations.

cond-mat.quant-gas↗

arXiv2020

Quantum Generalized Hydrodynamics

Physical systems made of many interacting quantum particles can often be described by Euler hydrodynamic equations in the limit of long wavelengths and low frequencies. Recently such a classical hydrodynamic framework, now dubbed Generalized Hydrodynamics (GHD), was found for quantum integrable models in one spatial dimension. Despite its great predictive power, GHD, like any Euler hydrodynamic equation, misses important quantum effects, such as quantum fluctuations leading to non-zero equal-time correlations between fluid cells at different positions. Focusing on the one-dimensional gas of bosons with delta repulsion, and on states of zero entropy, for which quantum fluctuations are larger, we reconstruct such quantum effects by quantizing GHD. The resulting theory of quantum GHD can be viewed as a multi-component Luttinger liquid theory, with a small set of effective parameters that are fixed by the Thermodynamic Bethe Ansatz. It describes quantum fluctuations of truly nonequilibrium systems where conventional Luttinger liquid theory fails.

cond-mat.quant-gas↗

arXiv2019

Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain

In a many-body quantum system, local operators in Heisenberg picture $O(t) = e^{i H t} O e^{-i H t}$ spread as time increases. Recent studies have attempted to find features of that spreading which could distinguish between chaotic and integrable dynamics. The operator entanglement - the entanglement entropy in operator space - is a natural candidate to provide such a distinction. Indeed, while it is believed that the operator entanglement grows linearly with time $t$ in chaotic systems, numerics suggests that it grows only logarithmically in integrable systems. That logarithmic growth has already been established for non-interacting fermions, however progress on interacting integrable systems has proved very difficult. Here, for the first time, a logarithmic upper bound is established rigorously for all local operators in such a system: the `Rule 54' qubit chain, a model of cellular automaton introduced in the 1990s [Bobenko et al., CMP 158, 127 (1993)], recently advertised as the simplest representative of interacting integrable systems. Physically, the logarithmic bound originates from the fact that the dynamics of the models is mapped onto the one of stable quasiparticles that scatter elastically; the possibility of generalizing this scenario to other interacting integrable systems is briefly discussed.

cond-mat.stat-mech↗

arXiv2019

Generalized HydroDynamics on an Atom Chip

The emergence of a special type of fluid-like behavior at large scales in one-dimensional (1d) quantum integrable systems, theoretically predicted in 2016, is established experimentally, by monitoring the time evolution of the in situ density profile of a single 1d cloud of $^{87}{\rm Rb}$ atoms trapped on an atom chip after a quench of the longitudinal trapping potential. The theory can be viewed as a dynamical extension of the thermodynamics of Yang and Yang, and applies to the whole range of repulsion strength and temperature of the gas. The measurements, performed on weakly interacting atomic clouds that lie at the crossover between the quasicondensate and the ideal Bose gas regimes, are in very good agreement with the 2016 theory. This contrasts with the previously existing 'conventional' hydrodynamic approach---that relies on the assumption of local thermal equilibrium---, which is unable to reproduce the experimental data.

cond-mat.quant-gas↗

arXiv2016

Conformal field theory of critical Casimir forces between surfaces with alternating boundary conditions in two dimensions

Systems as diverse as binary mixtures and inclusions in biological membranes, and many more, can be described effectively by interacting spins. When the critical fluctuations in these systems are constrained by boundary conditions, critical Casimir forces (CCF) emerge. Here we analyze CCF between boundaries with alternating boundary conditions in two dimensions, employing conformal field theory (CFT). After presenting the concept of boundary changing operators, we specifically consider two different boundary configurations for a strip of critical Ising spins: (I) alternating equi-sized domains of up and down spins on both sides of the strip, with a possible lateral shift, and (II) alternating domains of up and down spins of different size on one side and homogeneously fixed spins on the other side of the strip. Asymptotic results for the CCF at small and large distances are derived. We introduce a novel modified Szegö formula for determinants of real antisymmetric block Toeplitz matrices to obtain the exact CCF and the corresponding scaling functions at all distances. We demonstrate the existence of a surface Renormalization Group flow between universal force amplitudes of different magnitude and sign. The Casimir force can vanish at a stable equilibrium position that can be controlled by parameters of the boundary conditions. Lateral Casimir forces assume a universal simple cosine form at large separations.

cond-mat.stat-mech↗

arXiv2015

Critical Casimir Force between Inhomogeneous Boundaries

To study the critical Casimir force between chemically structured boundaries immersed in a binary mixture at its demixing transition, we consider a strip of Ising spins subject to alternating fixed spin boundary conditions. The system exhibits a boundary induced phase transition as function of the relative amount of up and down boundary spins. This transition is associated with a sign change of the asymptotic force and a diverging correlation length that sets the scale for the crossover between different universal force amplitudes. Using conformal field theory and a mapping to Majorana fermions, we obtain the universal scaling function of this crossover, and the force at short distances.

cond-mat.stat-mech↗

arXiv2012

Conformal boundary state for the rectangular geometry

We discuss conformal field theories (CFTs) in rectangular geometries, and develop a formalism that involves a conformal boundary state for the 1+1d open system. We focus on the case of homogeneous boundary conditions (no insertion of a boundary condition changing operator), for which we derive an explicit expression of the associated boundary state, valid for any arbitrary CFT. We check the validity of our solution, comparing it with known results for partition functions, numerical simulations of lattice discretizations, and coherent state expressions for free theories.

math-ph↗

arXiv2010

Bulk and boundary critical behaviour of thin and thick domain walls in the two-dimensional Potts model

The geometrical critical behaviour of the two-dimensional Q-state Potts model is usually studied in terms of the Fortuin-Kasteleyn (FK) clusters, or their surrounding loops. In this paper we study a quite different geometrical object: the spin clusters, defined as connected domains where the spin takes a constant value. Unlike the usual loops, the domain walls separating different spin clusters can cross and branch. Moreover, they come in two versions, "thin" or "thick", depending on whether they separate spin clusters of different or identical colours. For these reasons their critical behaviour is different from, and richer than, those of FK clusters. We develop a transfer matrix technique enabling the formulation and numerical study of spin clusters even when Q is not an integer. We further identify geometrically the crossing events which give rise to conformal correlation functions. We study the critical behaviour both in the bulk, and at a boundary with free, fixed, or mixed boundary conditions. This leads to infinite series of fundamental critical exponents, h_{l_1-l_2,2 l_1} in the bulk and h_{1+2(l_1-l_2),1+4 l_1} at the boundary, valid for 0 <= Q <= 4, that describe the insertion of l_1 thin and l_2 thick domain walls. We argue that these exponents imply that the domain walls are `thin' and `thick' also in the continuum limit. A special case of the bulk exponents is derived analytically from a massless scattering approach.

cond-mat.stat-mech↗

arXiv2010

Conformal field theory at central charge c=0: a measure of the indecomposability (b) parameters

A good understanding of conformal field theory (CFT) at c=0 is vital to the physics of disordered systems, as well as geometrical problems such as polymers and percolation. Steady progress has shown that these CFTs should be logarithmic, with indecomposable operator product expansions, and indecomposable representations of the Virasoro algebra. In one of the earliest papers on the subject, V. Gurarie introduced a single parameter b to quantify this indecomposability in terms of the logarithmic partner t of the stress energy tensor T. He and A. Ludwig conjectured further that b=-5/8 for polymers and b=5/6 for percolation. While a lot of physics may be hidden behind this parameter - which has also given rise to a lot of discussions - it had remained very elusive up to now, due to the lack of available methods to measure it experimentally or numerically, in contrast say with the central charge. We show in this paper how to overcome the many difficulties in trying to measure b. This requires control of a lattice scalar product, lattice Jordan cells, together with a precise construction of the state L_{-2}|0>. The final result is that b=5/6 for polymers. For percolation, we find that b=-5/8 within an XXZ or supersymmetric representation. In the geometrical representation, we do not find a Jordan cell for L_0 at level two (finite-size Hamiltonian and transfer matrices are fully diagonalizable), so there is no b in this case.

math-ph↗

arXiv2009

Exact solution of the anisotropic special transition in the O(n) model in 2D

The effect of surface exchange anisotropies is known to play a important role in magnetic critical and multicritical behavior at surfaces. We give an exact analysis of this problem in d=2 for the O(n) model by using Coulomb gas, conformal invariance and integrability techniques. We obtain the full set of critical exponents at the anisotropic special transition--where the symmetry on the boundary is broken down to O(n_1)xO(n-n_1)--as a function of n_1. We also obtain the full phase diagram and crossover exponents. Crucial in this analysis is a new solution of the boundary Yang-Baxter equations for loop models. The appearance of the generalization of Schramm-Loewner Evolution SLE_{κ,ρ} is also discussed.

cond-mat.stat-mech↗

arXiv2009

Conformal boundary conditions in the critical O(n) model and dilute loop models

We study the conformal boundary conditions of the dilute O(n) model in two dimensions. A pair of mutually dual solutions to the boundary Yang-Baxter equations are found. They describe anisotropic special transitions, and can be interpreted in terms of symmetry breaking interactions in the O(n) model. We identify the corresponding boundary condition changing operators, Virasoro characters, and conformally invariant partition functions. We compute the entropies of the conformal boundary states, and organize the flows between the various boundary critical points in a consistent phase diagram. The operators responsible for the various flows are identified. Finally, we discuss the relation to open boundary conditions in the O(n) model, and present new crossing probabilities for Ising domain walls.

math-ph↗

arXiv2008

Conformal two-boundary loop model on the annulus

We study the two-boundary extension of a loop model - corresponding to the dense phase of the O(n) model, or to the Q=n^2 state Potts model - in the critical regime -2 < n < 2. This model is defined on an annulus of aspect ratio τ. Loops touching the left, right, or both rims of the annulus are distinguished by arbitrary (real) weights which moreover depend on whether they wrap the periodic direction. Any value of these weights corresponds to a conformally invariant boundary condition. We obtain the exact seven-parameter partition function in the continuum limit, as a function of τ, by a combination of algebraic and field theoretical arguments. As a specific application we derive some new crossing formulae for percolation clusters.

math-ph↗