arXiv subjects

Nicolas Laflorencie

Publications and source records attributed to Nicolas Laflorencie.

At least 55 records · Page 3Linked to original sources

arXiv2017

Weak Versus Strong Disorder Superfluid-Bose Glass Transition in One Dimension

Using large-scale simulations based on matrix product state and quantum Monte Carlo techniques, we study the superfluid to Bose glass-transition for one-dimensional attractive hard-core bosons at zero temperature, across the full regime from weak to strong disorder. As a function of interaction and disorder strength, we identify a Berezinskii-Kosterlitz-Thouless critical line with two different regimes. At small attraction where critical disorder is weak compared to the bandwidth, the critical Luttinger parameter $K_c$ takes its universal Giamarchi-Schulz value $K_{c}=3/2$. Conversely, a non-universal $K_c>3/2$ emerges for stronger attraction where weak-link physics is relevant. In this strong disorder regime, the transition is characterized by self-similar power-law distributed weak links with a continuously varying characteristic exponent $α$.

cond-mat.dis-nn↗

arXiv2017

Extended slow dynamical regime close to the many-body localization transition

Many-body localization is characterized by a slow logarithmic growth of the entanglement entropy after a global quantum quench while the local memory of an initial density imbalance remains at infinite time. We investigate how much the proximity of a many-body localized phase can influence the dynamics in the delocalized ergodic regime where thermalization is expected. Using an exact Krylov space technique, the out-of-equilibrium dynamics of the random-field Heisenberg chain is studied up to $L=28$ sites, starting from an initially unentangled high-energy product state. Within most of the delocalized phase, we find a sub-ballistic entanglement growth $S(t)\propto t^{1/z}$ with a disorder-dependent exponent $z\ge1$, in contrast with the pure ballistic growth $z=1$ of clean systems. At the same time, anomalous relaxation is also observed for the spin imbalance ${\cal{I}}(t)\propto t^{-ζ}$ with a continuously varying disorder-dependent exponent $ζ$, vanishing at the transition. This provides a clear experimental signature for detecting this non-conventional regime.

cond-mat.dis-nn↗

arXiv2017

Quantum Monte Carlo detection of SU(2) symmetry breaking in the participation entropies of line subsystems

Using quantum Monte Carlo simulations, we compute the participation (Shannon-Rényi) entropies for groundstate wave functions of Heisenberg antiferromagnets for one-dimensional (line) subsystems of length $L$ embedded in two-dimensional ($L\times L$) square lattices. We also study the line entropy at finite temperature, i.e. of the diagonal elements of the density matrix, for three-dimensional ($L\times L\times L$) cubic lattices. The breaking of SU(2) symmetry is clearly captured by a universal logarithmic scaling term $l_q\ln L$ in the Rényi entropies, in good agreement with the recent field-theory results of Misguish, Pasquier and Oshikawa [arXiv:1607.02465]. We also study the dependence of the log prefactor $l_q$ on the Rényi index $q$ for which a transition is detected at $q_c\simeq 1$.

cond-mat.str-el↗

arXiv2017

Disorder-induced Revival of the Bose-Einstein Condensation in Ni(Cl$_{1-x}$Br$_x$)$_2$-4SC(NH$_2$)$_2$ at High Magnetic Fields

Building on recent NMR experiments [Phys. Rev. Lett. 118, 067203], we theoretically investigate the high magnetic field regime of the disordered quasi-one-dimensional $S=1$ antiferromagnetic material Ni(Cl$_{1-x}$Br$_x$)$_2$-4SC(NH$_2$)$_2$. The interplay between disorder, chemically controlled by Br-doping, interactions, and the external magnetic field, leads to a very rich phase diagram. Beyond the well-known antiferromagnetically ordered regime, analog of a Bose condensate of magnons, which disappears when $H\ge 12.3$ T, we unveil a resurgence of phase coherence at higher field $H\sim 13.6$ T, induced by the doping. Interchain couplings stabilize finite temperature long-range order whose extension in the field - temperature space is governed by the concentration of impurities $x$. Such a "mini-condensation" contrasts with previously reported Bose-glass physics in the same regime, and should be accessible to experiments.

cond-mat.str-el↗

arXiv2017

Nuclear Magnetic Resonance Reveals Disordered Level-Crossing Physics in the Bose-Glass Regime of the Br-doped Ni(Cl$_{1-x}$Br$_x$)$_2$-4SC(NH$_2$)$_2$ Compound at a High Magnetic Field

By measuring the nuclear magnetic resonance (NMR) 1/T_1 relaxation rate in the Br (bond) doped DTN compound, Ni(Cl(1-x)Br_x)2-4SC(NH2)2 (DTNX), we show that the low-energy spin dynamics of its high magnetic field "Bose-glass" regime is dominated by a strong peak of spin fluctuations found at the nearly doping-independent position H* = 13.6 T. From its temperature and field dependence we conclude that this corresponds to a level crossing of the energy levels related to the doping-induced impurity states. Observation of the local NMR signal from the spin adjacent to the doped Br allowed us to fully characterize this impurity state. We have thus quantified a microscopic theoretical model that paves the way to better understanding of the Bose-glass physics in DTNX, as revealed in the related theoretical study [M. Dupont, S. Capponi, and N. Laflorencie, Phys. Rev. Lett. 118, 067204 (2017), arXiv:1610.05136].

cond-mat.str-el↗

arXiv2017

Nuclear magnetic resonance study of the magnetic-field-induced ordered phase in the NiCl2-4SC(NH2)2 compound

Nuclear magnetic resonance (NMR) study of the high magnetic field (H) part of the Bose-Einstein condensed (BEC) phase of the quasi-onedimensional (quasi-1D) antiferromagnetic quantum spin-chain compound NiCl2-4SC(NH2)2 (DTN) was performed. We precisely determined the phase boundary, Tc(H), down to 40 mK; the critical boson density, n_c(Tc); and the absolute value of the BEC order parameter S_perp at very low temperature (T = 0.12 K). All results are accurately reproduced by numerical quantum Monte Carlo simulations of a realistic three-dimensional (3D) model Hamiltonian. Approximate analytical predictions based on the 1D Tomonaga-Luttinger liquid description are found to be precise for Tc(H), but less so for S_perp(H), which is more sensitive to the strength of 3D couplings, in particular close to the critical field. A mean-field treatment, based on the Hartree-Fock-Popov description, is found to be valid only up to n_c = 4% (T < 0.3 K), while for higher n_c boson interactions appear to modify the density of states.

cond-mat.str-el↗

arXiv2016

Temperature dependence of the NMR relaxation rate 1/T_1 for quantum spin chains

We present results of numerical simulations performed on one-dimensional spin chains in order to extract the so-called relaxation rate $1/T_1$ accessible through NMR experiments. Building on numerical tensor network methods using the Matrix Product States (MPS) formalism, we can follow the non-trivial crossover occurring in critical chains between the high-temperature diffusive classical regime and the low-temperature response described by the Tomonaga-Luttinger liquid (TLL) theory, for which analytical expressions are known. In order to compare analytics and numerics, we focus on a generic spin-$1/2$ XXZ chain which is a paradigm of gapless TLL, as well as a more realistic spin-$1$ anisotropic chain, modelling the DTN material, which can be either in a trivial gapped phase or in a TLL regime induced by an external magnetic field. Thus, by monitoring the finite temperature crossover, we provide quantitative limits on the range of validity of TLL theory, that will be useful when interpreting experiments on quasi one-dimensional materials.

cond-mat.str-el↗

arXiv2016

Dimensional modulation of spontaneous magnetic order in quasi-two-dimensional quantum antiferromagnets

Spontaneous symmetry breaking is deeply related to dimensionality of system. The Neel order going with spontaneous breaking of $U(1)$ symmetry is safely allowed at any temperature for three-dimensional systems but allowed only at zero temperature for purely two-dimensional systems. We closely investigate how smoothly the ordering process of the three-dimensional system is modulated into that of the two-dimensional one with reduction of dimensionality, considering spatially anisotropic quantum antiferromagnets. We first show that the Néel temperature is kept finite even in the two-dimensional limit although the Néel order is greatly suppressed for low-dimensionality. This feature of the Néel temperature is highly nontrivial, which dictates how the order parameter is squashed under the reduction of dimensionality. Next we investigate this dimensional modulation of the order parameter. We develop our argument taking as example a coupled spin-ladder system relevant for experimental studies. The ordering process is investigated multidirectionally using theoretical techniques of a mean-field method combined with analytical (exact solutions of quantum field theories) or numerial (density-matrix renormalization-group) method, a variational method, a renormalization-group study, linear spin-wave theory, and quantum Monte-Carlo simulation. We show that these methods independent of each other lead to the same conclusion about the dimensional modulation.

cond-mat.str-el↗

arXiv2016

Quantum entanglement in condensed matter systems

This review focuses on the field of quantum entanglement applied to condensed matter physics systems with strong correlations, a domain which has rapidly grown over the last decade. By tracing out part of the degrees of freedom of correlated quantum systems, useful and non-trivial informations can be obtained through the study of the reduced density matrix, whose eigenvalue spectrum (the entanglement spectrum) and the associated Rényi entropies are now well recognized to contains key features. In particular, the celebrated area law for the entanglement entropy of ground-states will be discussed from the perspective of its subleading corrections which encode universal details of various quantum states of matter, e.g. symmetry breaking states or topological order. Going beyond entropies, the study of the low-lying part of the entanglement spectrum also allows to diagnose topological properties or give a direct access to the excitation spectrum of the edges, and may also raise significant questions about the underlying entanglement Hamiltonian. All these powerful tools can be further applied to shed some light on disordered quantum systems where impurity/disorder can conspire with quantum fluctuations to induce non-trivial effects. Disordered quantum spin systems, the Kondo effect, or the many-body localization problem, which have all been successfully (re)visited through the prism of quantum entanglement, will be discussed in details. Finally, the issue of experimental access to entanglement measurement will be addressed, together with its most recent developments.

cond-mat.str-el↗

arXiv2015

Entanglement entropies of the $J_1 - J_2$ Heisenberg antiferromagnet on the square lattice

Using a modified spin-wave theory which artificially restores zero sublattice magnetization on finite lattices, we investigate the entanglement properties of the Néel ordered $J_1 - J_2$ Heisenberg antiferromagnet on the square lattice. Different kinds of subsystem geometries are studied, either corner-free (line, strip) or with sharp corners (square). Contributions from the $n_G=2$ Nambu-Goldstone modes give additive logarithmic corrections with a prefactor ${n_G}/{2}$ independent of the Rényi index. On the other hand, corners lead to additional (negative) logarithmic corrections with a prefactor $l^{c}_q$ which does depend on both $n_G$ and the Rényi index $q$, in good agreement with scalar field theory predictions. By varying the second neighbor coupling $J_2$ we also explore universality across the Néel ordered side of the phase diagram of the $J_1 - J_2$ antiferromagnet, from the frustrated side $0<J_2/J_1<1/2$ where the area law term is maximal, to the strongly ferromagnetic regime $-J_2/J_1\gg1$ with a purely logarithmic growth $S_q=\frac{n_G}{2}\ln N$, thus recovering the mean-field limit for a subsystem of $N$ sites. Finally, a universal subleading constant term $γ_q^{\rm ord}$ is extracted in the case of strip subsystems, and a direct relation is found (in the large-S limit) with the same constant extracted from free lattice systems. The singular limit of vanishing aspect ratios is also explored, where we identify for $γ_q^\text{ord}$ a regular part and a singular component, explaining the discrepancy of the linear scaling term for fixed width {\it{vs}} fixed aspect ratio subsystems.

cond-mat.str-el↗

arXiv2015

Universal logarithmic corrections to entanglement entropies in two dimensions with spontaneously broken continuous symmetries

We explore the Rényi entanglement entropies of a one-dimensional (line) subsystem of length $L$ embedded in two-dimensional $L\times L$ square lattice for quantum spin models whose ground-state breaks a continuous symmetry in the thermodynamic limit. Using quantum Monte Carlo simulations, we first study the $J_1 - J_2$ Heisenberg model with antiferromagnetic nearest-neighbor $J_1>0$ and ferromagnetic second-neighbor couplings $J_2\le 0$. The signature of SU(2) symmetry breaking on finite size systems, ranging from $L=4$ up to $L=40$ clearly appears as a universal additive logarithmic correction to the Rényi entanglement entropies: $l_q \ln L$ with $l_q\simeq 1$, independent of the Rényi index and values of $J_2$. We confirm this result using a high precision spin-wave analysis (with restored spin rotational symmetry) on finite lattices up to $10^5\times 10^5$ sites, allowing to explore further non-universal finite size corrections and study in addition the case of U(1) symmetry breaking. Our results fully agree with the prediction $l_q=n_G/2$ where $n_G$ is the number of Goldstone modes, by Metlitski and Grover [arXiv:1112.5166].

cond-mat.str-el↗

arXiv2014

Many-body localization edge in the random-field Heisenberg chain

We present a large scale exact diagonalization study of the one dimensional spin $1/2$ Heisenberg model in a random magnetic field. In order to access properties at varying energy densities across the entire spectrum for system sizes up to $L=22$ spins, we use a spectral transformation which can be applied in a massively parallel fashion. Our results allow for an energy-resolved interpretation of the many body localization transition including the existence of an extensive many-body mobility edge. The ergodic phase is well characterized by Gaussian orthogonal ensemble statistics, volume-law entanglement, and a full delocalization in the Hilbert space. Conversely, the localized regime displays Poisson statistics, area-law entanglement and non ergodicity in the Hilbert space where a true localization never occurs. We perform finite size scaling to extract the critical edge and exponent of the localization length divergence.

cond-mat.dis-nn↗

arXiv2014

Critical Properties of the Superfluid - Bose Glass Transition in Two Dimensions

We investigate the superfluid (SF) to Bose glass (BG) quantum phase transition using extensive quantum Monte Carlo simulations of two-dimensional hard-core bosons in a random box potential. $T=0$ critical properties are studied by thorough finite-size scaling of condensate and SF densities, both vanishing at the same critical disorder $W_c=4.80(5)$. Our results give the following estimates for the critical exponents: $z=1.85(15)$, $ν=1.20(12)$, $η=-0.40(15)$. Furthermore, the probability distribution of the SF response $P(\lnρ_{\rm sf})$ displays striking differences across the transition: while it narrows with increasing system sizes $L$ in the SF phase, it broadens in the BG regime, indicating an absence of self-averaging, and at the critical point $P(\lnρ_{\rm sf}+z \ln L)$ is scale invariant. Finally, high-precision measurements of the local density rule out a percolation picture for the SF-BG transition.

cond-mat.dis-nn↗

arXiv2014

Spin-resolved entanglement spectroscopy of critical spin chains and Luttinger liquids

Quantum critical chains are well described and understood by virtue of conformal field theory. Still the meaning of the real space entanglement spectrum -- the eigenvalues of the reduced density matrix -- of such systems remains in general elusive, even when there is an additional quantum number available such as spin or particle number. In this paper we explore in details the properties and the structure of the reduced density matrix of critical XXZ spin-$\frac{1}{2}$ chains. We investigate the quantum/thermal correspondence between the reduced density matrix of a $T=0$ pure quantum state and the thermal density matrix of an effective entanglement Hamiltonian. Using large scale DMRG and QMC simulations, we investigate the conformal structure of the spectra, the entanglement Hamiltonian and temperature. We then introduce the notion of spin-resolved entanglement entropies which display interesting scaling features.

cond-mat.str-el↗

arXiv2014

Fluctuations and Entanglement spectrum in quantum Hall states

The measurement of quantum entanglement in many-body systems remains challenging. One experimentally relevant fact about quantum entanglement is that in systems whose degrees of freedom map to free fermions with conserved total particle number, exact relations hold relating the Full Counting Statistics associated with the bipartite charge fluctuations and the sequence of R\' enyi entropies. We draw a correspondence between the bipartite charge fluctuations and the entanglement spectrum, mediated by the R\' enyi entropies. In the case of the integer quantum Hall effect, we show that it is possible to reproduce the generic features of the entanglement spectrum from a measurement of the second charge cumulant only. Additionally, asking whether it is possible to extend the free fermion result to the $ν=1/3$ fractional quantum Hall case, we provide numerical evidence that the answer is negative in general. We further address the problem of quantum Hall edge states described by a Luttinger liquid, and derive expressions for the spectral functions of the real space entanglement spectrum at a quantum point contact realized in a quantum Hall sample.

cond-mat.mes-hall↗

arXiv2014

Improving entanglement and thermodynamic Rényi entropy measurements in quantum Monte Carlo

We present a method for improving measurements of the entanglement Rényi entropies in quantum Monte Carlo simulations by relating them with measurements of participation Rényi entropies. Exploiting the capability of building improved estimators for the latter allows to obtain very good estimates for entanglement Rényi entropies. When considering a full system instead of a bipartition, the method can be further ameliorated providing access to the thermodynamic Rényi entropies with high accuracy. We also explore a recently-proposed method for the reconstruction of the entanglement spectrum from entanglement Rényi entropies and finally show how potential entanglement Hamiltonians may be tested for their validity using a comparison with thermal Rényi entropies.

cond-mat.str-el↗

arXiv2014

Participation spectroscopy and entanglement Hamiltonian of quantum spin models

Shannon-Rényi entropies and associated participation spectra quantify how much a many-body wave-function is localized in a given configuration basis. Using these tools, we present an analysis of the ground-state wave functions of various quantum spin systems in one and two dimensions. General ideas and a review of the current status of this field are first given, with a particular emphasis on universal subleading terms characterizing different quantum phases of matter, and associated transitions. We highlight the connection with the related entanglement entropies and spectra when this is possible. In a second part, new results are presented for the participation spectra of interacting spin models, mostly based on quantum Monte Carlo simulations, but also using perturbation theory in some cases. For full antiferromagnetic systems, participation spectra are analyzed in terms of ferromagnetic domain walls which experience a repulsive pairwise interaction. This confinement potential is either linear for long-range Néel order, or logarithmic for quasi-long-range order. The case of subsystems is also analyzed in great detail for a 2d dimerized Heisenberg model undergoing a quantum phase transition between a gapped paramagnet and a Néel phase. Participation spectra of line shaped (1d) sub-systems are quantitatively compared with finite temperature participation spectra of ansatz effective boundary (1d) entanglement Hamiltonians. While short-range models describe almost perfectly the gapped side, the Néel regime is best compared using long-range effective Hamiltonians. Spectral comparisons performed using Kullback-Leibler divergences, a tool potentially useful for entanglement spectra, provide a quantitative way to identify both the best boundary entanglement Hamiltonian and temperature.

cond-mat.str-el↗

arXiv2014

Chiral phases of two-dimensional hard-core bosons with frustrated ring-exchange

We study the zero temperature phase diagram of two-dimensional hard-core bosons on a square lattice with nearest neighbour and plaquette (ring-exchange) hoppings, at arbitrary densities, by means of a hierarchical mean-field theory. In the frustrated regime, where quantum Monte Carlo suffers from a sign problem, we find a rich phase diagram where exotic states with nonzero chirality emerge. Among them, novel insulating phases, characterized by nonzero bond-chirality and plaquette order, are found over a large region of the parameter space. In the unfrustrated regime, the hierarchical mean-field approach improves over the standard mean-field treatment as it is able to capture the transition from a superfluid to a valence bond state upon increasing the strength of the ring-exchange term, in qualitative agreement with quantum Monte Carlo results.

cond-mat.str-el↗