arXiv subjects

Gilles Parez

Publications and source records attributed to Gilles Parez.

At least 19 recordsLinked to original sources

arXiv2026

Universal scaling of spatially extended zero modes in inhomogeneous SSH chains

Protected zero modes are a hallmark of topological phases of matter and are exponentially localized at sharp interfaces between distinct gapped phases. We investigate how this picture changes for smooth interfaces in a broad class of inhomogeneous Su-Schrieffer-Heeger (SSH) models. Combining an exact lattice solution with an inhomogeneous Dirac description, we show that the associated Jackiw-Rebbi zero mode becomes spatially extended. For arbitrary smooth hopping profiles, its lattice extension universally scales as the square root of the system size, independently of the microscopic details of the interface. This emergent length defines a mesoscopic critical region separating two gapped phases, within which correlations decay algebraically before crossing over to exponential decay. In addition, the entanglement entropy scales as the logarithm of the emergent length near the interface, confirming the interpretation of a mesoscopic critical region. Our results establish a universal critical length governing the low-energy physics of smooth topological interfaces.

cond-mat.str-el↗

arXiv2025

Inhomogeneous SSH models and the doubling of orthogonal polynomials

We analyze Su-Schrieffer-Heeger (SSH) models using the doubling method for orthogonal polynomial sequences. This approach yields the analytical spectrum and exact eigenstates of the models. We demonstrate that the standard SSH model is associated with the doubling of Chebyshev polynomials. Extending this technique to the doubling of other finite sequences enables the construction of Hamiltonians for inhomogeneous SSH models which are exactly solvable. We detail the specific cases associated with Krawtchouk and $q$-Racah polynomials. This work highlights the utility of polynomial-doubling techniques in obtaining exact solutions for physical models.

math-ph↗

arXiv2025

Smearing of dynamical quantum phase transitions in dissipative free-fermion systems

We investigate the Lindblad dynamics of the reduced Loschmidt echo (RLE) in dissipative quadratic fermion systems. Focusing on the case of gain and loss dissipation, we derive general conditions for the persistence of nonanalyticities (so-called dynamical quantum phase transitions) in the time evolution of the RLE. We show that nonanalyticities that are present in the corresponding unitary dynamics can survive under purely gain or purely loss processes, but are completely smeared out as soon as both channels are active, even if one is infinitesimally small. These results hold for generic dissipative Gaussian evolutions, and are illustrated explicitly for the quench from the N\'eel state in the tight-binding chain, as well as for the quantum Ising chain. We also show that the subtle interplay between dissipative and unitary dynamics gives rise to a nested lightcone structure in the dynamics of the RLE, even in cases where this structure is not present in the corresponding unitary evolution, due to coherent cancellations in the phase structure of the wavefunction.

cond-mat.stat-mech↗

arXiv2025

Reduced fidelities for free fermions out of equilibrium: From dynamical quantum phase transitions to Mpemba effect

We investigate the out-of-equilibrium dynamics after a quantum quench of the reduced fidelities between the states of a subregion $A$ at different times. Precisely, we consider the fidelity between the time-dependent state of $A$ and its initial value, as well as with the state at infinite time. We denote these fidelities as the reduced Loschmidt echo (RLE) and the final-state fidelity (FSF), respectively. If region $A$ is the full system, the RLE coincides with the standard Loschmidt echo. We focus on quenches from Gaussian states in several instances of the XY spin chain. In the hydrodynamic limit of long times and large sizes of $A$, with their ratio fixed, the reduced fidelities admit a quasiparticle picture interpretation. Interestingly, for some quenches in the hydrodynamic regime the RLE features a complicated structure with an infinite sequence of nested lightcones, corresponding to quasiparticles with arbitrary large group velocities. This leads to a ''staircase'' of cusp-like singularities in the time-derivative of the fidelity. At the sub-hydrodynamic regime for some quenches the RLE exhibits cusp-like singularities, similar to the so-called dynamical quantum phase transitions (DQPT). We conjecture a criterion for the occurrence of the DQPT and for the ''critical'' times at which the singularities occur. Finally, we discuss the hydrodynamic limit of the FSF. In particular, we show that it provides a valuable tool to detect the so-called quantum Mpemba effect.

cond-mat.stat-mech↗

arXiv2025

Entanglement of Inhomogeneous Free Bosons and Orthogonal Polynomials

In this paper, we investigate the ground-state entanglement entropy in inhomogeneous free-boson models in one spatial dimension. We develop a powerful method to extract the leading term in the entanglement scaling, based on the analytic properties of the inhomogeneous potential. This method is applicable to a broad class of models with smooth spatial inhomogeneities. As a case study, we apply this approach for a family of exactly-solvable models characterized by orthogonal polynomials of the Askey scheme, finding a perfect match between the numerical and analytical results.

cond-mat.stat-mech↗

arXiv2024

Entanglement Hamiltonian and orthogonal polynomials

We study the entanglement Hamiltonian for free-fermion chains with a particular form of inhomogeneity. The hopping amplitudes and chemical potentials are chosen such that the single-particle eigenstates are related to discrete orthogonal polynomials of the Askey scheme. Due to the bispectral properties of these functions, one can construct an operator which commutes exactly with the entanglement Hamiltonian and corresponds to a linear or parabolic deformation of the physical one. We show that this deformation is interpreted as a local inverse temperature and can be obtained in the continuum limit via methods of conformal field theory. Using this prediction, the properly rescaled eigenvalues of the commuting operator are found to provide a very good approximation of the entanglement spectrum and entropy.

cond-mat.stat-mech↗

arXiv2024

Distinctive features of inhomogeneous spin chains

This review presents recent developments in the study of inhomogeneous XX spin chains, highlighting results on perfect state transfer, out-of-equilibrium stationary dynamics in open systems, and entanglement and correlations in ground states. We discuss the conditions on couplings that enable perfect state transfer, examine how heat currents scale when the chains are coupled to thermal baths, explore the role of tridiagonal matrices in approximating the entanglement Hamiltonian and investigate bulk and boundary entanglement negativity and correlation decay. These findings underscore some of the distinctive physical behavior of inhomogeneous spin chains and their potential applications in quantum information and thermal transport.

quant-ph↗

arXiv2024

Separable ellipsoids around multipartite states

We show that, in finite dimensions, around any $m$-partite product state $\rho_{\rm prod}=\rho_1\otimes...\otimes\rho_m$, there exists an ellipsoid of separable states centered around $\rho_{\rm prod}$. This separable ellipsoid contains the separable ball proposed in previous works, and the volume of the ellipsoid is typically exponentially larger than that of the ball, due to the hierarchy of eigenvalues in typical states. We further generalize this ellipsoidal criterion to a trace formula that yields separable region around all separable states, and further study biseparability. Our criteria not only help numerical procedures to rigorously detect separability, but they also lead to a nested hierarchy of SLOCC-stable subsets that cover the separable set. We apply the procedure for separability detection to 3-qubit X states, genuinely entangled 4-qubit states mixed with noise, and the 1d transverse field Ising model at finite temperature to illustrate the power of our procedure for understanding entanglement in physical systems.

quant-ph↗

arXiv2024

Fermionic logarithmic negativity in the Krawtchouk chain

The entanglement of non-complementary regions is investigated in an inhomogeneous free-fermion chain through the lens of the fermionic logarithmic negativity. Focus is on the Krawtchouk chain, whose relation to the eponymous orthogonal polynomials allows for exact diagonalization and analytical calculations of certain correlation functions. For adjacent regions, the negativity scaling corresponds to that of a conformal field theory with central charge $c=1$, in agreement with previous studies on bipartite entanglement in the Krawtchouk chain. For disjoint regions, we focus on the skeletal regime where each region reduces to a single site. This regime is sufficient to extract the leading behaviour at large distances. In the bulk, the negativity decays as $d^{-4 \Delta_f}$ with $\Delta_f=1/2$, where $d$ is the separation between the regions. This is in agreement with the homogeneous result of free Dirac fermions in one dimension. Surprisingly, when one site is close to the boundary, this exponent changes and depends on the parity of the boundary site $m=0,1,2,\dots$, with $\Delta_f^{\textrm{even}}=3/8$ and $\Delta_f^{\textrm{odd}}=5/8$. The results are supported by numerics and analytical calculations.

cond-mat.stat-mech↗

arXiv2024

The Fate of Entanglement

Quantum entanglement manifests itself in non-local correlations between the constituents of a system. In its simplest realization, a measurement on one subsystem is affected by a prior measurement on its partner, irrespective of their separation. For multiple parties, purely collective types of entanglement exist but their detection, even theoretically, remains an outstanding open question. Here, we argue that all forms of multipartite entanglement entirely disappear during the typical evolution of a physical state as it heats up, evolves in time in a large family of dynamical protocols, or as its parts become separated. We focus on the generic case where the system interacts with an environment. These results mainly follow from the geometry of the entanglement-free continent in the space of physical states, and hold in great generality. We illustrate these phenomena with a frustrated molecular quantum magnet in and out of equilibrium, and a quantum spin chain. In contrast, if the particles are fermions, such as electrons, another notion of entanglement exists that protects bipartite quantum correlations. However, genuinely collective fermionic entanglement disappears during typical evolution, thus sharing the same fate as in bosonic systems. These findings provide fundamental knowledge about the structure of entanglement in quantum matter and architectures, paving the way for its manipulation.

quant-ph↗

arXiv2024

Entanglement of free-fermion systems, signal processing and algebraic combinatorics

This paper offers a review of recent studies on the entanglement of free-fermion systems on graphs that take advantage of methods pertaining to signal processing and algebraic combinatorics. On the one hand, a parallel with time and band limiting problems is used to obtain a tridiagonal matrix commuting with the chopped correlation matrix in bispectral situations and on the other, the irreducible decomposition of the Terwilliger algebra arising in the context of $P$-polynomial association schemes is seen to yield a simplifying framework.

quant-ph↗

arXiv2023

Entanglement negativity between separated regions in quantum critical systems

We study the entanglement between disjoint subregions in quantum critical systems through the lens of the logarithmic negativity. We work with systems in arbitrary dimensions, including conformal field theories and their corresponding lattice Hamiltonians, as well as resonating valence-bond states. At small separations, the logarithmic negativity is big and displays universal behavior, but we show non-perturbatively that it decays faster than any power at large separations. This can already be seen in the minimal setting of single-spin subregions. The corresponding absence of distillable entanglement at large separations generalizes the 1d result, and indicates that quantum critical groundstates do not possess long-range bipartite entanglement, at least for bosons. For systems with fermions, a more suitable definition of the logarithmic negativity exists that takes into account fermion parity, and we show that it decays algebraically. Along the way we obtain general results for the moments of the partially transposed density matrix.

cond-mat.str-el↗

arXiv2023

Reflected entropy and computable cross-norm negativity: Free theories and symmetry resolution

We investigate a separability criterion based on the computable cross-norm (CCNR), and a related quantity called the CCNR negativity. We introduce a reflected version of the CCNR negativity, and discuss its connection with other well-established entanglement-related quantities, namely the reflected entropy and the operator entanglement entropy. For free fermionic and bosonic theories, we derive exact formulas in terms of two-point correlation functions, which allow for systematic numerical investigations and, in principle, analytical treatments. For systems with a global $U(1)$ symmetry, we study the symmetry-resolved reflected entropy and CCNR negativity. We provide conformal field theory (CFT) results for the charged moments in the case of adjacent intervals, finding perfect agreement with the numerics. We observe an equipartition of reflected entropies and CCNR negativities, both for free-fermions and free-boson models. The first charge-dependent corrections are conjectured for fermions, and worked out from the CFT calculations for bosons.

hep-th↗

arXiv2023

Absence of logarithmic enhancement in the entanglement scaling of free fermions on folded cubes

This study investigates the scaling behavior of the ground-state entanglement entropy in a model of free fermions on folded cubes. An analytical expression is derived in the large-diameter limit, revealing a strict adherence to the area law. The absence of the logarithmic enhancement expected for free fermions is explained using a decomposition of folded cubes in chains based on its Terwilliger algebra and $\mathfrak{so}(3)_{-1}$. The entanglement Hamiltonian and its relation to Heun operators are also investigated.

cond-mat.stat-mech↗

arXiv2022

Separability and entanglement of resonating valence-bond states

We investigate separability and entanglement of Rokhsar-Kivelson (RK) states and resonating valence-bond (RVB) states. These states play a prominent role in condensed matter physics, as they can describe quantum spin liquids and quantum critical states of matter, depending on their underlying lattices. For dimer RK states on arbitrary tileable graphs, we prove the exact separability of the reduced density matrix of $k$ disconnected subsystems, implying the absence of bipartite and multipartite entanglement between the subsystems. For more general RK states with local constraints, we argue separability in the thermodynamic limit, and show that any local RK state has zero logarithmic negativity, even if the density matrix is not exactly separable. In the case of adjacent subsystems, we find an exact expression for the logarithmic negativity in terms of partition functions of the underlying statistical model. For RVB states, we show separability for disconnected subsystems up to exponentially small terms in the distance $d$ between the subsystems, and that the logarithmic negativity is exponentially suppressed with $d$. We argue that separability does hold in the scaling limit, even for arbitrarily small ratio $d/L$, where $L$ is the characteristic size of the subsystems. Our results hold for arbitrary lattices, and encompass a large class of RK and RVB states, which include certain gapped quantum spin liquids and gapless quantum critical systems.

cond-mat.str-el↗

arXiv2022

Multipartite information of free fermions on Hamming graphs

We investigate multipartite information and entanglement measures in the ground state of a free-fermion model defined on a Hamming graph. Using the known diagonalization of the adjacency matrix, we solve the model and construct the ground-state correlation matrix. Moreover, we find all the eigenvalues of the chopped correlation matrix when the subsystem consists of $n$ disjoint Hamming subgraphs embedded in a larger one. These results allow us to find an exact formula for the entanglement entropy of disjoint graphs, as well as for the mutual and tripartite information. We use the exact formulas for these measures to extract their asymptotic behavior in two distinct thermodynamic limits, and find excellent match with the numerical calculations. In particular, we find that the entanglement entropy admits a logarithmic violation of the area law which decreases the amount of entanglement compared to the area law scaling.

quant-ph↗

arXiv2022

Analytical results for the entanglement dynamics of disjoint blocks in the XY spin chain

The study of the dynamics of entanglement measures after a quench has become a very active area of research in the last two decades, motivated by the development of experimental techniques. However, exact results in this context are available in only very few cases. In this work, we present the proof of the quasiparticle picture for the dynamics of entanglement entropies for two disjoint blocks in the XY chain after a quantum quench. As a byproduct, we also prove the quasiparticle conjecture for the mutual information in that model. Our calculations generalize those presented in [M. Fagotti, P. Calabrese, Phys. Rev. A 78, 010306 (2008)] to the case where the correlation matrix is a block-Toeplitz matrix, and rely on the multidimensional stationary phase approximation in the scaling limit. We also test the quasiparticle predictions against exact numerical calculations, and find excellent agreement. In the case of three blocks, we show that the tripartite information vanishes when at least two blocks are adjacent.

cond-mat.stat-mech↗

arXiv2022

Symmetry-resolved R\'enyi fidelities and quantum phase transitions

We introduce a family of quantum R\'enyi fidelities and discuss their symmetry resolution. We express the symmetry-resolved fidelities as Fourier transforms of charged fidelities, for which we derive exact formulas for Gaussian states. These results also yield a formula for the total fidelities of Gaussian states, which we expect to have applications beyond the scope of this paper. We investigate the total and symmetry-resolved fidelities in the XX spin chain, and focus on (i) fidelities between thermal states, and (ii) fidelities between reduced density matrices at zero temperature. Both thermal and reduced fidelities can detect the quantum phase transition of the XX spin chain. Moreover, we argue that symmetry-resolved fidelities are sensitive to the inner structure of the states. In particular, they can detect the phase transition through the reorganisation of the charge sectors at the critical point. This a main feature of symmetry-resolved fidelities which we expect to be general. We also highlight that reduced fidelities can detect quantum phase transitions in the thermodynamic limit.

cond-mat.stat-mech↗