arXiv subjects

Nicolas Laflorencie

Publications and source records attributed to Nicolas Laflorencie.

At least 19 recordsLinked to original sources

arXiv2026

Unconventional Quantum Criticality in Long-Range Spin-1 Chains: Insights from Entanglement Entropy and Bipartite Fluctuations

We study the ground-state phase diagram of a spin-1 Heisenberg chain with staggered long-range (LR) interactions decaying as $\propto r^{-\alpha}$ using a quantum Monte Carlo approach based on the split-spin representation. This formulation enables efficient large-scale simulations by mapping the spin-1 model onto spin-$1/2$ degrees of freedom with local projection constraints. We resolve the continuous quantum phase transition between the gapped Haldane phase at large $\alpha$ (short-range regime) and a gapless antiferromagnetically ordered N\'eel phase at small $\alpha$ (LR regime), where the continuous SU(2) symmetry is broken. From finite-size scaling and crossing point analyses, we determine the critical point to be at $\alpha_c = 2.49(1)$ and extract the associated critical exponents, which indicate unconventional criticality. In particular, the transition is found to be nonconformal, characterized by a dynamical exponent $z \neq 1$. We further analyze the scaling of entanglement entropy and bipartite fluctuations across the transition, and determine the corresponding universal scalings in both phases and at criticality.

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arXiv2026

Strong zero modes in random Ising-Majorana chains

We investigate the fate and robustness of topological strong zero modes (SZMs) in random Ising-Majorana chains using the SZM fidelity, ${\cal F}_{\rm SZM}$, as a many-body diagnostic that quantifies how accurately SZM operators map the {\it entire} spectrum between opposite parity sectors. In clean systems, ${\cal F}_{\rm SZM}=1$ in the topological phase, vanishes in the trivial regime, and takes the universal value $\sqrt{8}/\pi$ at the $(1+1)$D Ising critical point. Here we study how quenched disorder modifies this picture across the infinite-randomness fixed point (IRFP) governing the criticality of the random chain. In both microcanonical and canonical ensembles, SZMs persist throughout the topological phase, including the gapless Griffiths regime, with fidelities converging exponentially to unity. At the IRFP, however, the fidelity distributions become ensemble dependent: the microcanonical ensemble displays bimodal peaks at $\{0.5,1\}$, while the canonical ensemble develops a triple-peak structure at $\{0,0.5,1\}$ with power-law singularities. Our results establish ${\cal F}_{\rm SZM}$ as a robust probe of localization-protected topological order and uncover distinctive topological features of infinite-randomness criticality. Unlike the clean Ising CFT, where the finite critical value arises from a cancellation of power laws, the IRFP seems to exhibit an intrinsically stronger topological character. The edge-selective structure of the critical distributions may suggest a boundary manifestation of the average Kramers-Wannier duality symmetry at the IRFP.

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arXiv2026

Beyond the imbalance: site-resolved dynamics probing resonances in many-body localization

We explore the limitations of using imbalance dynamics as a diagnostic tool for many-body localization (MBL) and show that spatial averaging can mask important microscopic features. Focusing on the strongly disordered regime of the random-field XXZ chain, we use state-of-the-art numerical techniques (Krylov time evolution and full diagonalization) to demonstrate that site-resolved spin autocorrelators reveal a rich and complex dynamical behavior that is obscured by the imbalance observable. By analyzing the time evolution and infinite-time limits of these local probes, we reveal resonant structures and rare local instabilities within the MBL phase. These numerical findings are supported by an analytical, few-site toy model that captures the emergence of a multiple-peak structure in local magnetization histograms, which is a hallmark of local resonances. These few-body local effects provide a more detailed understanding of ergodicity-breaking dynamics, and also allow us to explain the finite-size effects of long-time imbalance, and its sensitivity to the initial conditions in quench protocols. Overall, our experimentally testable predictions highlight the necessity of a refined, site-resolved approach to fully understand the complexities of MBL and its connection to rare-region effects.

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arXiv2025

Extreme statistics as a probe of the superfluid to Bose-glass Berezinskii-Kosterlitz-Thouless transition

Recent studies of delocalization-localization transitions in disordered quantum chains have highlighted the role of rare, chain-breaking events that favor localization, in particular for high-energy eigenstates related to many-body localization. In this context, we revisit the random-field XXZ spin-1/2 chain at zero temperature with ferromagnetic interactions, equivalent to interacting fermions or hard-core bosons in a random potential with attractive interactions. We argue that localization in this model can be characterized by chain-breaking events, which are probed by the extreme values of simple local observables, such as the on-site density or the local magnetization, that are readily accessible in both experiments and numerical simulations. Adopting a bosonic language, we study the disorder-induced Berezinskii-Kosterlitz-Thouless (BKT) quantum phase transition from superfluid (SF) to Bose glass (BG), and focus on the strong disorder regime where localization is driven by weak links. Based on high-precision density matrix renormalization group simulations, we numerically show that extreme local densities accurately capture the BKT transition, even for relatively short chains ranging from a few dozen to a hundred sites. We also discuss the SF-BG transition in the weak disorder regime, where finite-size effects pose greater challenges. Overall, our work seeks to establish a solid foundation for using extreme statistics of local observables, such as density, to probe delocalization-localization transitions in disordered quantum chains, both in the ground state and at high energy.

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arXiv2025

Critical Berezinskii-Kosterlitz-Thouless dynamics in the archetypal two-dimensional spin system Ba$_2$CuSi$_2$O$_6$Cl$_2$

We study the spin dynamics in the quasi-2D spin-$1/2$ dimer compound Ba$_2$CuSi$_2$O$_6$Cl$_2$, which exhibits a magnetic field-induced Bose-Einstein condensate (BEC) of triplons. Using nuclear magnetic resonance spin-lattice relaxation rate ($T_1^{-1}$) measurements combined with large-scale quantum Monte Carlo (QMC) simulations, we investigate critical fluctuations across the field-temperature phase diagram. Bridging the behavior observed in 1D and 3D systems, the $T_1^{-1}$ relaxation rate shows a pronounced peak extending well above the N\'eel temperature $T_N$, indicating strong two-dimensional Berezinskii-Kosterlitz-Thouless (BKT)-type fluctuations. A quantitative match between experimental and theoretical BEC phase boundaries validates an effective XXZ model. The study determines the intrinsic BKT transition temperature $T_{\mathrm{BKT}}$ from QMC, revealing a nearly field-independent $T_{\mathrm{BKT}}/T_N \approx 0.74$. Scaling analysis of the relaxation rate shows critical exponents consistent with 2D universality, and a narrow temperature window is identified where 2D physics dominates. These findings establish Ba$_2$CuSi$_2$O$_6$Cl$_2$ as a model system for exploring BKT dynamics in quantum magnets.

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arXiv2025

Long-range resonances in quasiperiodic many-body localization

We investigate long-range resonances in quasiperiodic many-body localized (MBL) systems. Focusing on the Heisenberg chain in a deterministic Aubry-Andr\'{e} potential, we complement standard diagnostics by analyzing the structure of long-distance pairwise correlations at high energy. Contrary to the expectation that the ergodic-MBL transition in quasiperiodic systems should be sharper due to the absence of Griffiths regions, we uncover a broad unconventional regime at strong quasiperiodic potential, characterized by fat-tailed distributions of longitudinal correlations at long distance. This reveals the presence of atypical eigenstates with strong long-range correlations in a regime where standard diagnostics indicate stable MBL. We further identify these anomalous eigenstates as quasi-degenerate pairs of resonant cat states, which exhibit entanglement at long distance. These findings advance the understanding of quasiperiodic MBL and identify density-correlation measurements in ultracold atomic systems as a probe of long-range resonances.

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arXiv2025

Large deviations in the many-body localization transition: The case of the random-field XXZ chain

The effect of rare system-wide resonances in the many-body localization (MBL) transition has recently attracted significant attention. They are expected to play a prominent role in the stability of the MBL phase, prompting the development of new theoretical frameworks to properly account for their statistical weight. We employ a method based on an analogy with mean-field disordered glassy systems to characterize the statistics of transmission amplitudes between distant many-body configurations in Hilbert space, and apply it to the random-field XXZ spin chain. By introducing a Lagrange multiplier, which formally plays the role of an effective temperature controlling the influence of extreme outliers in the heavy-tailed distribution of propagators, we identify three distinct regimes: (i) an ergodic phase with uniform spreading in Hilbert space, (ii) an intermediate regime where delocalization is driven by rare, disorder-dependent long-range resonances, and (iii) a robust MBL phase where such resonances cannot destabilize localization. We derive a finite-size phase diagram in the disorder--interaction plane both in the spin and in the Anderson basis that quantitatively agrees with recent numerical results based on real-space spin-spin correlation functions. We further demonstrate that even infinitesimal interactions can destroy the Anderson insulator at finite disorder, with the critical disorder remaining finite down to small interaction strengths. By visualizing resonant transmission pathways on the Hilbert space graph, we provide a complementary perspective to real-space and spectral probes, revealing how the destabilization of the MBL phase at finite sizes stems from the emergence of resonant paths that become progressively rarer and shorter-ranged deep in the localized phase.

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arXiv2025

Unconventional Thermalization of a Localized Chain Interacting with an Ergodic Bath

The study of many-body localized (MBL) phases intrinsically links spectral properties with eigenstate characteristics: localized systems exhibit Poisson level statistics and area-law entanglement entropy, while ergodic systems display volume-law entanglement and follow random matrix theory predictions, including level repulsion. Here, we introduce the interacting Anderson Quantum Sun model, which significantly deviates from these conventional expectations. In addition to standard localized and ergodic phases, we identify a regime that exhibits volume-law entanglement coexisting with intermediate spectral statistics. We also identify another nonstandard regime marked by Poisson level statistics, sub-volume entanglement growth, and rare-event-dominated correlations, indicative of emerging ergodic instabilities. These results highlight unconventional routes of ergodicity breaking and offer fresh perspectives on how Anderson localization may be destabilized.

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arXiv2025

Cat states carrying long-range correlations in the many-body localized phase

Despite considerable efforts over the last decade, the high-energy phase diagram of the random-field Heisenberg chain still eludes our understanding, in particular the nature of the non-ergodic many-body localized (MBL) regime expected at strong disorder. In this work, we revisit this paradigmatic model by studying the statistics of rare atypical events of strongly correlated spin pairs traversing the entire system. They occur for unexpectedly strong disorder, i.e., in a regime where standard estimates fail to detect any instability. We then identify these very peculiar high-energy eigenstates, which exhibit system-wide ${\cal{O}}(1)$ correlations, as nearly degenerate pairs of resonant cat states of the form $|{\Phi}_{\pm}\rangle\sim {|{\alpha_1}\rangle}\pm {|{\alpha_2}\rangle}$, where ${|{\alpha_1}\rangle}$ and ${|{\alpha_2}\rangle}$ are spin basis states. We propose a simple and generic analytical description of this new class of eigenstates that exhibit system-spanning entanglement. This analytical ansatz guides us in our search for rare hidden cat states in exponentially large many-body spectra. This also enables a systematic numerical inspection of the microscopic anatomy of these unconventional pairs, which appear in a wide range of disorder strengths. In the light of recent studies and ongoing debates on the MBL problem, our results offer new perspectives and stimulating challenges to this very active field.

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arXiv2025

Ground states of quasi-two-dimensional correlated systems via energy expansion

We introduce a generic method for computing groundstates that is applicable to a wide range of spatially anisotropic 2D many-body quantum systems. By representing the 2D system using a low-energy 1D basis set, we obtain an effective 1D Hamiltonian that only has quasi-local interactions, at the price of a large local Hilbert space. We apply our new method to three specific 2D systems of weakly coupled chains: hardcore bosons, a spin-$1/2$ Heisenberg Hamiltonian, and spinful fermions with repulsive interactions. In particular, we showcase a non-trivial application of the energy expansion framework, to the anisotropic triangular Heisenberg lattice, a highly challenging model related to 2D spin liquids. Treating lattices of unprecedented size, we provide evidence for the existence of a quasi-1D gapless spin liquid state in this system. We also demonstrate the energy expansion-framework to perform well where external validation is possible. For the fermionic benchmark in particular, we showcase the energy expansion-framework's ability to provide results of comparable quality at a small fraction of the resources required for previous computational efforts.

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arXiv2024

Statistics of systemwide correlations in the random-field XXZ chain: Importance of rare events in the many-body localized phase

Motivated by recent debates around the many-body localization (MBL) problem, and in particular its stability against systemwide resonances, we investigate long-distance spin-spin correlations across the phase diagram of the random-field XXZ model, with a particular focus on the strong disorder regime. Building on state-of-the-art shift-invert diagonalization techniques, we study the high-energy behavior of transverse and longitudinal correlation functions, computed at the largest possible distance, for a broad range of disorder and interaction strengths. Our results show that while transverse correlations display a fairly stable exponential decay over the entire XXZ phase diagram, longitudinal correlations exhibit markedly different behavior, revealing distinct physical regimes. More precisely, we identify an intermediate disorder region where standard observables show well-converged MBL behavior [J. Colbois et al., Phys. Rev. Lett. 133, 116502 (2024)] while the distributions of longitudinal correlations reveal unexpected fat-tails towards large values. These rare events strongly influence the average decay of longitudinal correlations, which we find to be algebraic in a broad region inside the supposed MBL phase, whereas the typical decay remains mostly exponential. At stronger disorder and weaker interactions, this intermediate regime is replaced by a more conventional exponential decay with short correlation lengths for both typical and average correlators, as expected for standard localization. Our findings shed light on the systemwide instabilities and raise important questions about the impact of such rare but large long-range correlations on the stability of the MBL phase. Finally, we discuss the possible fate of the intermediate region in the context of recent perspectives in the field.

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arXiv2024

Unconventional Scalings of Quantum Entropies in Long-Range Heisenberg Chains

In this work, building on state-of-the-art quantum Monte Carlo simulations, we perform systematic finite-size scaling of both entanglement and participation entropies for long-range Heisenberg chain with unfrustrated power-law decaying interactions. We find distinctive scaling behaviors for both quantum entropies in the various regimes explored by tuning the decay exponent $\alpha$, thus capturing non-trivial features through logarithmic terms, beyond the case of linear Nambu-Goldstone modes. Our systematic analysis reveals that the quantum entanglement information, hidden in the scaling of the two studied entropies, can be obtained to the same level of order parameters and other usual finite-size observables of quantum many-body lattice models. The analysis and results obtained here can readily apply to more quantum criticalities in 1D and 2D systems.

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arXiv2024

Interaction-Driven Instabilities in the Random-Field XXZ Chain

Despite enormous efforts devoted to the study of the many-body localization (MBL) phenomenon, the nature of the high-energy behavior of the Heisenberg spin chain in a strong random magnetic field is lacking consensus. Here, we take a step back by exploring the weak interaction limit starting from the Anderson localized (AL) insulator. Through shift-invert diagonalization, we find that below a certain disorder threshold $h^*$, weak interactions necessarily lead to ergodic instability, whereas at strong disorder the AL insulator directly turns into MBL. This agrees with a simple interpretation of the avalanche theory for restoration of ergodicity. We further map the phase diagram for the generic XXZ model in the disorder $h$ -- interaction $\Delta$ plane. Taking advantage of the total magnetization conservation, our results unveil the remarkable behavior of the spin-spin correlation functions: in the regime indicated as MBL by standard observables, their exponential decay undergoes a unique inversion of orientation $\xi_z>\xi_x$. We find that the longitudinal length $\xi_z$ is a key quantity for capturing ergodic instabilities, as it increases with system size near the thermal phase, in sharp contrast to its transverse counterpart $\xi_x$.

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arXiv2024

Universal features of entanglement entropy in the honeycomb Hubbard model

The entanglement entropy is a unique probe to reveal universal features of strongly interacting many-body systems. In two or more dimensions these features are subtle, and detecting them numerically requires extreme precision, a notoriously difficult task. This is especially challenging in models of interacting fermions, where many such universal features have yet to be observed. In this paper we tackle this challenge by introducing a new method to compute the Rényi entanglement entropy in auxiliary-field quantum Monte Carlo simulations, where we treat the entangling region itself as a stochastic variable. We demonstrate the efficiency of this method by extracting, for the first time, universal subleading logarithmic terms in a two dimensional model of interacting fermions, focusing on the half-filled honeycomb Hubbard model at $T=0$. We detect the universal corner contribution due to gapless fermions throughout the Dirac semi-metal phase and at the Gross-Neveu-Yukawa critical point, where the latter shows a pronounced enhancement depending on the type of entangling cut. Finally, we observe the universal Goldstone mode contribution in the antiferromagnetic Mott insulating phase.

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arXiv2023

Absence of a direct metal to Mott insulator transition for disordered interacting fermions on the Cayley tree

Interacting fermions in the presence of disorder pose one of the most challenging problems in condensed matter physics, primarily due to the absence of accurate numerical tools. Our investigation delves into the intricate interplay between interaction-induced Mott insulation and disorder-driven Anderson localization in the Hubbard model subjected to a random potential. On the Cayley tree, the application of statistical dynamical mean-field theory proves adept at discerning among a metal and the two distinct insulators, Anderson or Mott. Our comprehensive analysis, accounting for subtle yet potent finite-size effects and fluctuations, yields a noteworthy finding: in the presence of disorder, we consistently observe an intervening Anderson-localized regime between the metallic and Mott insulator states. This observation intriguingly mirrors scenarios witnessed in dirty Bosons, where an insulating Bose glass phase consistently emerges between the superfluid and Mott phases.

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arXiv2023

Universal signatures of Majorana zero modes in critical Kitaev chains

Many topological or critical aspects of the Kitaev chain are well known, with several classic results. In contrast, the study of the critical behavior of the strong Majorana zero modes (MZM) has been overlooked. Here we introduce two topological markers which, surprisingly, exhibit non-trivial signatures over the entire (1+1) Ising critical line. We first analytically compute the MZM fidelity ${\cal{F}}_{\rm MZM}$--a measure of the MZM mapping between parity sectors. It takes a universal value along the (1+1) Ising critical line, ${\cal{F}}_{\rm MZM}=\sqrt{8}/π$, independent of the energy. We also obtain an exact analytical result for the critical MZM occupation number ${\cal N}_{\rm MZM}$ which depends on the Catalan's constant ${\cal G}\approx 0.91596559$, for both the ground-state (${\cal N}_{\rm MZM}=1/2-4{\cal{G}}/π^2\approx 0.12877$) and the first excited state (${\cal N}_{\rm MZM}=1/2+(8-4{\cal{G}})/π^2\approx 0.93934$). We further compute finite-size corrections which identically vanish for the special ratio $Δ/t=\sqrt{2}-1$ between pairing and hopping in the critical Kitaev chain.

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arXiv2023

Breaking the chains: extreme value statistics and localization in random spin chains

Despite a very good understanding of single-particle Anderson localization in one-dimensional (1D) disordered systems, many-body effects are still full of surprises, a famous example being the interaction-driven many-body localization (MBL) problem, about which much has been written, and perhaps the best is yet to come. Interestingly enough the non-interacting limit provides a natural playground to study non-trivial multiparticle physics, offering the possibility to test some general mechanisms with very large-scale exact diagonalization simulations. In this work, we first revisit the 1D many-body Anderson insulator through the lens of extreme value theory, focusing on the extreme polarizations of the equivalent spin chain model in a random magnetic field. A many-body-induced chain breaking mechanism is explored numerically, and compared to an analytically solvable toy model. A unified description, from weak to large disorder strengths $W$ emerges, where the disorder-dependent average localization length $ξ(W)$ governs the extreme events leading to chain breaks. In particular, tails of the local magnetization distributions are controlled by $ξ(W)$. Remarkably, we also obtain a quantitative understanding of the full distribution of the extreme polarizations, which is given by a Fréchet-type law. In a second part, we explore finite interaction physics and the MBL question. For the available system sizes, we numerically quantify the difference in the extreme value distributions between the interacting problem and the non-interacting Anderson case. Strikingly, we observe a sharp "extreme-statistics transition" as $W$ changes, which may coincide with the MBL transition.

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arXiv2023

Resilient infinite randomness criticality for a disordered chain of interacting Majorana fermions

The quantum critical properties of interacting fermions in the presence of disorder are still not fully understood. While it is well known that for Dirac fermions, interactions are irrelevant to the non-interacting infinite randomness fixed point (IRFP), the problem remains largely open in the case of Majorana fermions which further display a much richer disorder-free phase diagram. Here, pushing the limits of DMRG simulations, we carefully examine the ground-state of a Majorana chain with both disorder and interactions. Building on appropriate boundary conditions and key observables such as entanglement, energy gap, and correlations, we strikingly find that the non-interacting Majorana IRFP is very stable against finite interactions, in contrast with previous claims.

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