arXiv subjects

Loïc Herviou

Publications and source records attributed to Loïc Herviou.

At least 19 recordsLinked to original sources

arXiv2026

Finite-state automata for exact matrix product operators of tight-binding Hamiltonians: fractals, quasicrystals, trees and hyperbolic lattices

Inspired by the recent progress in the simulation of tight-binding Hamiltonians on large lattices using tensor networks, we introduce a systematic matrix product operator (MPO) construction for single-particle Hamiltonians on recursively structured lattices. Taking advantage of this recursive structure, we encode the lattice geometry in a finite-state automaton and, adapting ideas from Abelian-symmetric tensor networks, obtain an exact and analytical MPO representation of the Hamiltonian, where the number of tensors grows logarithmically with the system size and the bond dimension is set by the number of automaton states. Several examples demonstrate the generality of the framework: regular lattices, fractals, Cayley trees, hyperbolic lattices, and one- and two-dimensional Fibonacci quasicrystals. Combined with the kernel polynomial method, these MPO representations enable large-scale calculations of spectral properties without explicitly constructing the full Hamiltonian. This provides a unified route to the exploration of electronic properties across a broad class of lattices at exponentially large system sizes.

cond-mat.mes-hall↗

arXiv2026

From weakly to strongly-interacting driven-dissipative bosons in one dimension

We consider a one-dimensional driven-dissipative Bose-Hubbard model subjected to incoherent pump and one- and two-body losses, and analyze it by studying its two-point space-time correlations. By employing a combination of numerical methods, such as stochastic semi-classical simulations and tensor network methods, as well as perturbation theory within the Keldysh formalism, we characterize the system at varying filling and interaction strength. We present results for two complementary regimes: i) at large filling and weak interactions, where we show that Kardar-Parisi-Zhang scaling is visible in the linewidth of the spectral function and ii) at weak filling and strong interactions, where we analyze what remains of the mean field transition and identify a change of nature of the excitations. Our study covers two important regions of the phase diagram of such a system.

cond-mat.quant-gas↗

arXiv2026

Exact Diagonalization, Matrix Product States and Conformal Perturbation Theory Study of a 3D Ising Fuzzy Sphere Model

Numerical studies of phase transitions in statistical and quantum lattice models provide crucial insights into the corresponding Conformal Field Theories (CFTs). In higher dimensions, comparing finite-volume numerical results to infinite-volume CFT data is facilitated by choosing the sphere $S^{d-1}$ as the spatial manifold. Recently, the fuzzy sphere regulator in Ref. [Zhu et al, Phys. Rev. X 13 021009 (2023)] has enabled such studies with exact rotational invariance, yielding impressive agreement with known 3D Ising CFT predictions, as well as new results. However, systematic improvements and a deeper understanding of finite-size corrections remain essential. In this work, we revisit the fuzzy sphere regulator, focusing on the original Ising model, with two main goals. First, we assess the robustness of this approach using Conformal Perturbation Theory (CPT), to which we provide a detailed guidebook. We demonstrate how CPT provides a unified framework for determining the critical point, the speed of light, and residual deviations from CFT predictions. Applying this framework, we study finite-size corrections and clarify the role of tuning the model in minimizing these effects. Second, we develop a novel method for extracting Operator Product Expansion (OPE) coefficients from fuzzy sphere data. This method leverages the sensitivity of energy levels to detuning from criticality, providing new insights into level mixing and avoided crossings in finite systems. Our work also includes validation of CPT in a 1+1D Ising model away from the integrable limit.

cond-mat.stat-mech↗

arXiv2026

When and why non-Hermitian eigenvalues miss eigenstates in topological physics

Non-Hermitian systems exhibit a fundamental spectral dichotomy absent in Hermitian physics: the eigenvalue spectrum and the eigenstate spectrum can deviate significantly in the thermodynamic limit. We explain how non-Hermitian Hamiltonians can support eigenstates completely undetected by eigenvalues, with the unidirectional Hatano-Nelson model serving as both a minimal realization and universal paradigm for this phenomenon. Through exact analytical solutions, we show that this model contains not only hidden modes but multiple macroscopic hidden exceptional points that appear more generally in all systems with a non-trivial bulk winding. Our framework explains how the apparent bulk-edge correspondence failures in models like the non-Hermitian SSH chain instead reflect the systematic inability of the eigenvalue spectrum to detect certain eigenstates in systems with a skin-effect. These results establish the limitation of the eigenvalue spectrum and suggest how the eigenstate approach can lead to improved characterization of non-Hermitian topology.

cond-mat.mes-hall↗

arXiv2026

$\mathbb{Z}_L$ symmetry breaking in SU(N) Fermi-Hubbard dots at zero and finite temperature

We address the SU(N) Fermi-Hubbard model on a chain, with $N$ the number of degenerate orbitals, or colors, for each fermion. In the limit of both large number of colors $N$ and particles, and small number of sites $L \geq 2$, the model is proved to undergo a $\mathbb{Z}_L$ symmetry breaking for attractive local interaction amplitude $U$. Using a combination of Exact Diagonalization with full SU(N) symmetry, generalized L-levels Holstein-Primakoff transformation, Hartree-Fock method and large-N saddle point approximation of the partition function, we extend the results obtained in [PRA 111, L020201 (2025)] to $L \geq 3$ and finite temperature $T>0$. In particular, we show that at $T=0$ for $U<U_c\sim -1/N$, the ground state is L-fold degenerate, while for positive temperatures, the critical temperature is both proportional to $N$ and $U$, i.e. $T_c \propto -U N$, making this phase transition particularly suitable for large-N fermions.

cond-mat.str-el↗

arXiv2025

Universal Characterization of Quantum Many-Body States through Local Information

We propose a universal framework for classifying quantum states based on their scale-resolved correlation structure. Using the recently introduced information lattice, which provides an operational definition of the total amount of correlations at each scale, we define intrinsic characteristic length scales of quantum states. We analyze ground and midspectrum eigenstates of the disordered interacting Kitaev chain, showing that our framework provides a novel unbiased approach to quantum matter.

quant-ph↗

arXiv2025

A Model for Topological p-wave Superconducting Wires with Disorder and Interactions

We present a comprehensive theoretical study of interacting and disordered topological phases of coupled Kitaev wires, which may support further realistic applications of Majorana fermions. We develop a variety of analytical, mathematical and numerical methods for one and two-coupled wires, associated with a topological marker accessible from real-space correlation functions on the wire(s). We verify the stability of the topological superconducting phase and quantify disorder effects close to the quantum phase transitions, e.g. through two-point correlation functions or using a renormalization group (RG) analysis of disorder. We show for the first time that the double critical Ising (DCI) phase -- a fractional Majorana liquid characterized by a pair of half central charges and topological numbers -- is stabilized by strong interactions against disorder which respects the inversion symmetry between the wires (ie. parity conservation on each wire). In the presence of an inter-wire hopping term, the DCI phase turns into a protected topological phase with a bulk gap. We study the localization physics developing along the critical line for weaker interactions.

cond-mat.supr-con↗

arXiv2024

Singularity with and without disorder at AKLT points

The Affleck-Kennedy-Lieb-Tasaki (AKLT) point of the bilinear-biquadratic spin-1 chain is a cornerstone example of a disorder point where short-range correlations become incommensurate, and correlation lengths and momenta are non-analytic. While the presence of singularities appears to be generic for AKLT points, we show that for a family of SU(N) models, the AKLT point is not a disorder point: It occurs entirely within an incommensurate phase yet the wave vector remains singular on both sides of the AKLT point. We conjecture that this new possibility is generic for models where the representation is not self-conjugate and the transfer matrix non-Hermitian, while for self-conjugate representations the AKLT points remain disorder points.

cond-mat.str-el↗

arXiv2024

Ultraslow Growth of Number Entropy in an l-bit Model of Many-Body Localization

We demonstrate that slow growth of the number entropy following a quench from a local product state is consistent with many-body localization. To do this we construct a random circuit l-bit model with exponentially localized l-bits and exponentially decaying interactions between them. We observe an ultraslow growth of the number entropy starting from a Néel state, saturating at a value that grows with system size. This suggests that the observation of such growth in microscopic models is not sufficient to rule out many-body localization.

cond-mat.dis-nn↗

arXiv2024

Numerical investigation of the structure factors of the Read-Rezayi series

We numerically investigate the guiding center stucture factors of several states in the Read-Rezayi family. Using exact diagonalizations on the torus and density matrix renormalization group on an infinite cylinder, we test a conjecture proposed in [Can et al, Phys. Rev. Lett. 113 (2014)] for the $ν= \frac{3}{5}$ and $ν= \frac{4}{6}$ Read-Rezayi states. Furthermore, we discuss the strong finite-size effects present in numerically accessible wavefunctions, and provide a simple recipe to minimize them on manifolds where non-Abelian theories have topological degeneracies.

cond-mat.str-el↗

arXiv2023

Even-odd effects in the $J_1-J_2$ SU($N$) Heisenberg spin chain

The zero-temperature phase diagram of the $J_1-J_2$ SU($N$) antiferromagnetic Heisenberg spin chain is investigated by means of complementary field theory and numerical approaches for general $N$. A fully gapped SU($N$) valence bond solid made of $N$ sites is formed above a critical value of $J_2/J_1$ for all $N$. We find that the extension of this $N$-merized phase for larger values of $J_2$ strongly depends on the parity of $N$. For even $N$, the phase smoothly interpolates to the large $J_2$ regime where the model can be viewed as a zigzag SU($N$) two-leg spin ladder. The phase exhibits both a $N$-merized ground state and incommensurate spin-spin correlations. In stark contrast to the even case, we show that the $N$-merized phase with odd $N$ only has a finite extent with no incommensuration. A gapless phase in the SU($N$)$_1$ universality class is stabilized for larger $J_2$ that stems from the existence of a massless renormalization group flow from SU($N$)$_2$ to SU($N$)$_1$ conformal field theories when $N$ is odd.

cond-mat.str-el↗

arXiv2023

Fractional Topology in Interacting 1D Superconductors

We investigate the topological phases of two one-dimensional (1D) interacting superconducting wires and propose topological markers directly measurable from ground state correlation functions. These quantities remain powerful tools in the presence of couplings and interactions. We show with the density matrix renormalization group that the double critical Ising (DCI) phase discovered in [1] is a fractional topological phase with gapless Majorana modes in the bulk, and a one-half topological invariant per wire. Using both numerics and quantum field theoretical methods, we show that the phase diagram remains stable in the presence of an inter-wire hopping amplitude $t_{\bot}$ at length scales below $\sim 1/t_{\bot}$. A large inter-wire hopping amplitude results in the emergence of two integer topological phases, stable also at large interactions. They host one edge mode per boundary shared between both wires. At large interactions, the two wires are described by Mott physics, with the $t_{\bot}$ hopping amplitude resulting in a paramagnetic order.

cond-mat.str-el↗

arXiv2022

Possible restoration of particle-hole symmetry in the 5/2 Quantized Hall State at small magnetic field

Motivated by the experimental observation of a quantized 5/2 thermal conductance at filling $ν=5/2$, a result incompatible with both the Pfaffian and the Antipfaffian states, we have pushed the expansion of the effective Hamiltonian of the $5/2$ quantized Hall state to third-order in the parameter $κ=E_c/\hbar ω_c \propto 1/\sqrt{B}$ controlling the Landau level mixing , where $E_c$ is the Coulomb energy and $ω_c$ the cyclotron frequency. Exact diagonalizations of this effective Hamiltonian show that the difference in overlap with the Pfaffian and the AntiPfaffian induced at second-order is reduced by third-order corrections and disappears around $κ=0.4$, suggesting that these states are much closer in energy at smaller magnetic field than previously anticipated. Furthermore, we show that in this range of $κ$ the finite-size spectrum is typical of a quantum phase transition, with a strong reduction of the energy gap and with level crossings between excited states. These results point to the possibility of a quantum phase transition at smaller magnetic field into a phase with an emergent particle-hole symmetry that would explain the measured $5/2$ thermal conductance of the $5/2$ quantized Hall state.

cond-mat.str-el↗

arXiv2022

Time-evolution of local information: thermalization dynamics of local observables

Quantum many-body dynamics generically results in increasing entanglement that eventually leads to thermalization of local observables. This makes the exact description of the dynamics complex despite the apparent simplicity of (high-temperature) thermal states. For accurate but approximate simulations one needs a way to keep track of essential (quantum) information while discarding inessential one. To this end, we first introduce the concept of the information lattice, which supplements the physical spatial lattice with an additional dimension and where a local Hamiltonian gives rise to well defined locally conserved von Neumann information current. This provides a convenient and insightful way of capturing the flow, through time and space, of information during quantum time evolution, and gives a distinct signature of when local degrees of freedom decouple from long-range entanglement. As an example, we describe such decoupling of local degrees of freedom for the mixed field transverse Ising model. Building on this, we secondly construct algorithms to time-evolve sets of local density matrices without any reference to a global state. With the notion of information currents, we can motivate algorithms based on the intuition that information for statistical reasons flow from small to large scales. Using this guiding principle, we construct an algorithm that, at worst, shows two-digit convergence in time-evolutions up to very late times for diffusion process governed by the mixed field transverse Ising Hamiltonian. While we focus on dynamics in 1D with nearest-neighbor Hamiltonians, the algorithms do not essentially rely on these assumptions and can in principle be generalized to higher dimensions and more complicated Hamiltonians.

quant-ph↗

arXiv2021

Fate of the non-Hermitian skin effect in many-body fermionic systems

We revisit the fate of the skin modes in many-body non-Hermitian fermionic systems. Contrary to the single-particle case, the many-body ground state cannot exhibit an exponential localization of all eigenstates due to the Pauli exclusion principle. However, asymmetry can still exist in the density profile, which can be quantified using the imbalance between the two halves of the system. Using the non-Hermitian Su-Schrieffer-Heeger (SSH) chain as an illustration, we show the existence of two distinct scaling regimes for the imbalance. In the first one, the imbalance grows linearly with the system size, as generically expected. In the second one, the imbalance saturates to a finite value. By combining high-precision exact diagonalization calculations and analytical arguments, we observe that the imbalance does not scale when the occupied bands can be deformed to their Hermitian limit. This suggests a direct connection between the corresponding bulk topological invariants and the skin effect in many-body systems. Importantly, this relation also holds for interacting systems.

cond-mat.mes-hall↗

arXiv2020

Many-body localization in a fragmented Hilbert space

We study many-body localization (MBL) in a pair-hopping model exhibiting strong fragmentation of the Hilbert space. We show that several Krylov subspaces have both ergodic statistics in the thermodynamic limit and a dimension that scales much slower than the full Hilbert space, but still exponentially. Such a property allows us to study the MBL phase transition in systems including more than $50$ spins. The different Krylov spaces that we consider show clear signatures of a many-body localization transition, both in the Kullback-Leibler divergence of the distribution of their level spacing ratio and their entanglement properties. But they also present distinct scalings with system size. Depending on the subspace, the critical disorder strength can be nearly independent of the system size or conversely show an approximately linear increase with the number of spins.

cond-mat.dis-nn↗

arXiv2020

$\mathcal{L}^2$ localization landscape for highly-excited states

The localization landscape gives direct access to the localization of bottom-of-band eigenstates in non-interacting disordered systems. We generalize this approach to eigenstates at arbitrary energies in systems with or without internal degrees of freedom by introducing a modified $\mathcal{L}^2$-landscape, and we demonstrate its accuracy in a variety of archetypal models of Anderson localization in one and two dimensions. This $\mathcal{L}^2$-landscape function can be efficiently computed using hierarchical methods that allow evaluating the diagonal of a well-chosen Green function. We compare our approach to other landscape methods, bringing new insights on their strengths and limitations. Our approach is general and can in principle be applied to both studies of topological Anderson transitions and many-body localization.

cond-mat.dis-nn↗

arXiv2019

Entanglement spectrum and symmetries in non-Hermitian fermionic non-interacting models

We study the properties of the entanglement spectrum in gapped non-interacting non-Hermitian systems, and its relation to the topological properties of the system Hamiltonian. Two different families of entanglement Hamiltonians can be defined in non-Hermitian systems, depending on whether we consider only right (or equivalently only left) eigenstates or a combination of both left and right eigenstates. We show that their entanglement spectra can still be computed efficiently, as in the Hermitian limit. We discuss how symmetries of the Hamiltonian map into symmetries of the entanglement spectrum depending on the choice of the many-body state. Through several examples in one and two dimensions, we show that the biorthogonal entanglement Hamiltonian directly inherits the topological properties of the Hamiltonian for line gapped phases, with characteristic singular and energy zero modes. The right (left) density matrix carries distinct information on the topological properties of the many-body right (left) eigenstates themselves. In purely point gapped phases, when the energy bands are not separable, the relation between the entanglement Hamiltonian and the system Hamiltonian breaks down.

cond-mat.mes-hall↗