arXiv subjects

Grégoire Misguich

Publications and source records attributed to Grégoire Misguich.

34 records · Page 2Linked to original sources

arXiv2017

Out-of-equilibrium dynamics in a quantum impurity model: numerics for particle transport and entanglement entropy

We investigate the out-of-equilibrium properties of a simple quantum impurity model, the interacting resonant level model (IRLM). We focus on the scaling regime, where the bandwidth of the fermions in the leads is larger than all the other energies, so that the lattice and the continuum versions of the model become equivalent. Using time-dependent DMRG simulations initialized with states having different densities in the two leads we extend the results of Boulat, Saleur and Schmitteckert [Phys. Rev. Lett. 101, 140601 (2008)] concerning the current-voltage ($I$-$V$) curves, for several values of the interaction strength $U$. We estimate numerically the Kondo scale $T_B$ and the exponent $b(U)$ associated to the tunneling of the fermions from the leads to the dot. Next we analyze the quantum entanglement properties of the steady states. We focus in particular on the entropy rate $α$, describing the linear growth with time of the bipartite entanglement in the system. We show that, as for the current, $α/T_B$ is described by some function of $U$ and of the rescaled bias $V/T_B$. Finally, the spatial structure of the entropy profiles is discussed.

cond-mat.str-el↗

arXiv2017

Finite-size scaling of the Shannon-Rényi entropy in two-dimensional systems with spontaneously broken continuous symmetry

We study the scaling of the (basis dependent) Shannon entropy for two-dimensional quantum antiferromagnets with Néel long-range order. We use a massless free-field description of the gapless spin wave modes and phase space arguments to treat the fact that the finite-size ground state is rotationally symmetric, while there are degenerate physical ground states which break the symmetry. Our results show that the Shannon entropy (and its Rényi generalizations) possesses some universal logarithmic term proportional to the number $N_\text{NG}$ of Nambu-Goldstone modes. In the case of a torus, we show that $S_{n>1} \simeq {\rm const.} N+ \frac{N_\text{NG}}{4}\frac{n}{n-1} \ln{N}$ and $S_1 \simeq {\rm const.} N - \frac{N_\text{NG}}{4} \ln{N}$, where $N$ is the total number of sites and $n$ the Rényi index. The result for $n>1$ is in reasonable agreement with the quantum Monte Carlo results of Luitz et al. [Phys. Rev. Lett. 112, 057203 (2014)], and qualitatively similar to those obtained previously for the entanglement entropy. The Shannon entropy of a line subsystem (embedded in the two-dimensional system) is also considered. Finally, we present some density-matrix renormalization group (DMRG) calculations for a spin$\frac{1}{2}$ XY model on the square lattice in a cylinder geometry. These numerical data confirm our findings for logarithmic terms in the $n=\infty$ Rényi entropy (also called $-\ln{p_{\rm max}}$). They also reveal some universal dependence on the cylinder aspect ratio, in good agreement with the fact that, in that case, $p_{\rm max}$ is related to a non-compact free-boson partition function in dimension 1+1.

cond-mat.str-el↗

arXiv2016

Inverse participation ratios in the XXZ spin chain

We investigate numerically the inverse participation ratios in a spin-1/2 XXZ chain, computed in the "Ising" basis (i.e., eigenstates of $σ^z_i$). We consider in particular a quantity $T$, defined by summing the inverse participation ratios of all the eigenstates in the zero magnetization sector of a finite chain of length $N$, with open boundary conditions. From a dynamical point of view, $T$ is proportional to the stationary return probability to an initial basis state, averaged over all the basis states (initial conditions). We find that $T$ exhibits an exponential growth, $T\sim\exp(aN)$, in the gapped phase of the model and a linear scaling, $T\sim N$, in the gapless phase. These two different behaviors are analyzed in terms of the distribution of the participation ratios of individual eigenstates. We also investigate the effect of next-nearest-neighbor interactions, which break the integrability of the model. Although the massive phase of the non-integrable model also has $T\sim\exp(aN)$, in the gapless phase $T$ appears to saturate to a constant value.

cond-mat.str-el↗

arXiv2016

Flux quench in a system of interacting spinless fermions in one dimension

We study a quantum quench in a one-dimensional spinless fermion model (equivalent to the XXZ spin chain), where a magnetic flux is suddenly switched off. This quench is equivalent to imposing a pulse of electric field and therefore generates an initial particle current. This current is not a conserved quantity in presence of a lattice and interactions and we investigate numerically its time-evolution after the quench, using the infinite time-evolving block decimation method. For repulsive interactions or large initial flux, we find oscillations that are governed by excitations deep inside the Fermi sea. At long times we observe that the current remains non-vanishing in the gapless cases, whereas it decays to zero in the gapped cases. Although the linear response theory (valid for a weak flux) predicts the same long-time limit of the current for repulsive and attractive interactions (relation with the zero-temperature Drude weight), larger nonlinearities are observed in the case of repulsive interactions compared with that of the attractive case.

cond-mat.stat-mech↗

arXiv2013

Non-equilibrium steady states in the quantum XXZ spin chain

We investigate the dynamics of a critical XXZ spin-1/2 chain prepared in an inhomogeneous initial state with different magnetizations on the left and right halves. We simulate the real-time evolution using the time-evolving block decimation (TEBD) method. We follow the front propagation by measuring the magnetization and entanglement entropy profiles, and we focus on the situation where the initial state is not fully polarized. At long times, as in the free fermion case (T. Antal et al. 1999), a large central region develops where correlations become time-independent and translation invariant. The shape and speed of the fronts is studied numerically and we evaluate the stationary current as a function of initial magnetic field and as a function of the anisotropy Δ. We compare the results with the conductance of a Tomonaga-Luttinger liquid, and with the exact free-fermion solution at Δ=0. We also investigate the two-point correlations in the stationary region and find a good agreement with the "twisted" form obtained by J. Lancaster and A. Mitra (2010) using bosonization. Some deviations are nevertheless observed for strong currents.

cond-mat.str-el↗

arXiv2013

Time-reversal-symmetry-breaking chiral spin liquids: a projective symmetry group approach of bosonic mean-field theories

Projective symmetry groups (PSG) are the mathematical tools which allow to list and classify mean-field spin liquids (SL) based on a parton construction. The seminal work of Wen and its subsequent extension to bosons by Wang and Vishwanath concerned the so-called symmetric SL: i.e. states that break neither lattice symmetries nor time reversal invariance. Here we generalize this approach to chiral (time reversal symmetry breaking) SL described in a Schwinger boson mean-field approach. A special emphasis is put on frustrated lattices (triangular and kagome lattices), where the possibility of a chiral SL ground state has recently been discussed. The PSG approach is detailed for the triangular lattice case. Results for other lattices are given in the appendices. The physical significance of gauge invariant quantities called fluxes is discussed both in the classical limit and in the quantum SL and their expressions in terms of spin observables are given.

cond-mat.str-el↗

arXiv2012

Schwinger boson mean field theory: numerics for the energy landscape and gauge excitations in two-dimensional antiferromagnets

We perform some systematic numerical search for Schwinger boson mean field states on square and triangular lattice clusters. We look for possible inhomogeneous ground states as well as low-energy excited saddle points. The spectrum of the Hessian is also computed for each solution. On the square lattice we find gapless U(1) gauge modes in the non-magnetic phase. In the Z_2 liquid phase of the triangular lattice we identify the topological degeneracy as well as vison states.

cond-mat.str-el↗

arXiv2012

Two-dimensional quantum antiferromagnets

This review presents some theoretical advances in the field of quantum magnetism in two-dimensional systems, and quantum spin liquids in particular. It is to be published as a chapter in the second edition of the book "Frustrated spin systems", edited by H. T. Diep (World-Scientific). The section (Sec. 7) devoted to the kagome antiferromagnet has been completely rewritten/updated, as well as the concluding section (Sec. 8). The other sections (Secs. 1-6) are unchanged from the first edition of the book (published in 2005)

cond-mat.str-el↗

arXiv2011

Rényi entanglement entropies in quantum dimer models : from criticality to topological order

Thanks to Pfaffian techniques, we study the Rényi entanglement entropies and the entanglement spectrum of large subsystems for two-dimensional Rokhsar-Kivelson wave functions constructed from a dimer model on the triangular lattice. By including a fugacity $t$ on some suitable bonds, one interpolates between the triangular lattice (t=1) and the square lattice (t=0). The wave function is known to be a massive $\mathbb Z_2$ topological liquid for $t>0$ whereas it is a gapless critical state at t=0. We mainly consider two geometries for the subsystem: that of a semi-infinite cylinder, and the disk-like setup proposed by Kitaev and Preskill [Phys. Rev. Lett. 96, 110404 (2006)]. In the cylinder case, the entropies contain an extensive term -- proportional to the length of the boundary -- and a universal sub-leading constant $s_n(t)$. Fitting these cylinder data (up to a perimeter of L=32 sites) provides $s_n$ with a very high numerical accuracy ($10^{-9}$ at t=1 and $10^{-6}$ at $t=0.5$). In the topological $\mathbb{Z}_2$ liquid phase we find $s_n(t>0)=-\ln 2$, independent of the fugacity $t$ and the Rényi parameter $n$. At t=0 we recover a previously known result, $s_n(t=0)=-(1/2)\ln(n)/(n-1)$ for $n<1$ and $s_n(t=0)=-\ln(2)/(n-1)$ for $n>1$. In the disk-like geometry -- designed to get rid of the boundary contributions -- we find an entropy $s^{\rm KP}_n(t>0)=-\ln 2$ in the whole massive phase whatever $n>0$, in agreement with the result of Flammia {\it et al.} [Phys. Rev. Lett. 103, 261601 (2009)]. Some results for the gapless limit $R^{\rm KP}_n(t\to 0)$ are discussed.

cond-mat.stat-mech↗

arXiv2011

Competing Valence Bond Crystals in the Kagome Quantum Dimer Model

The singlet dynamics which plays a major role in the physics of the spin-1/2 Quantum Heisenberg Antiferromagnet (QHAF) on the Kagome lattice can be approximately described by projecting onto the nearest-neighbor valence bond (NNVB) singlet subspace. We re-visit here the effective Quantum Dimer Model which originates from the latter NNVB-projected Heisenberg model via a non-perturbative Rokhsar-Kivelson-like scheme. By using Lanczos exact diagonalisation on a 108-site cluster supplemented by a careful symmetry analysis, it is shown that a previously-found 36-site Valence Bond Crystal (VBC) in fact competes with a new type of 12-site "{\it resonating-columnar}" VBC. The exceptionally large degeneracy of the GS multiplets (144 on our 108-site cluster) might reflect the proximity of the Z_2 dimer liquid. Interestingly, these two VBC "emerge" in {\it different topological sectors}. Implications for the interpretation of numerical results on the QHAF are outlined.

cond-mat.str-el↗

arXiv2011

Phase transition in the Rényi-Shannon entropy of Luttinger liquids

The Rényi-Shannon entropy associated to critical quantum spins chain with central charge $c=1$ is shown to have a phase transition at some value $n_c$ of the Rényi parameter $n$ which depends on the Luttinger parameter (or compactification radius R). Using a new replica-free formulation, the entropy is expressed as a combination of single-sheet partition functions evaluated at $n-$ dependent values of the stiffness. The transition occurs when a vertex operator becomes relevant at the boundary. Our numerical results (exact diagonalizations for the XXZ and $J_1-J_2$ models) are in agreement with the analytical predictions: above $n_c=4/R^2$ the subleading and universal contribution to the entropy is $\ln(L)(R^2-1)/(4n-4)$ for open chains, and $\ln(R)/(1-n)$ for periodic ones (R=1 at the free fermion point). The replica approach used in previous works fails to predict this transition and turns out to be correct only for $n<n_c$. From the point of view of two-dimensional Rokhsar-Kivelson states, the transition reveals a rich structure in the entanglement spectra.

cond-mat.str-el↗

arXiv2011

Lattice symmetries and regular states in classical frustrated antiferromagnets

We consider some classical and frustrated lattice spin models with global O(3) spin symmetry. There is no general analytical method to find a ground-state if the spin dependence of the Hamiltonian is more than quadratic (i.e. beyond the Heisenberg model) and/or if the lattice has more than one site per unit cell. To deal with these situations, we introduce a family of variational spin configurations, dubbed "regular states", which respect all the lattice symmetries modulo global O(3) spin transformations (rotations and/or spin flips). The construction of these states is explicited through a group theoretical approach, and all the regular states on the square, triangular, honeycomb and kagome lattices are listed. Their equal time structure factors and powder-averages are shown for comparison with experiments. All the well known Néel states with 2 or 3 sublattices appear amongst regular states on various lattices, but the regular states also encompass exotic non-planar states with cubic, tetrahedral or cuboctahedral geometry of the T=0 order parameter. Whatever the details of the Hamiltonian (with the same symmetry group), a large fraction of these regular states are energetically stationary with respect to small deviations of the spins. In fact these regular states appear as exact ground-states in a very large range of parameter space of the simplest models that we have been looking at. As examples, we display the variational phase diagrams of the J1-J2-J3 Heisenberg model on all the previous lattices as well as that of the J1-J2-K ring-exchange model on square and triangular lattices.

cond-mat.str-el↗

arXiv2010

Geometric entanglement of critical XXZ and Ising chains and Affleck-Ludwig boundary entropies

We study the geometrical entanglement of the XXZ chain in its critical regime. Recent numerical simulations [Q.-Q. Shi, R. Orús, J. O. Fjærestad and H.-Q Zhou, New J. Phys. {\bf 12}, 025008 (2010)] indicate that it scales linearly with system size, and that the first subleading correction is constant, which was argued to be possibly universal. In this work, we confirm the universality of this number, by relating it to the Affleck-Ludwig boundary entropy corresponding to a Neumann boundary condition for a free compactified field. We find that the subleading constant is a simple function of the compactification radius, in agreement with the numerics. As a further check, we compute it exactly on the lattice at the XX point. We also discuss the case of the Ising chain in transverse field and show that the geometrical entanglement is related to the Affleck-Ludwig boundary entropy associated to a ferromagnetic boundary condition.

cond-mat.stat-mech↗

arXiv2010

Rényi entropy of a line in two-dimensional Ising models

We consider the two-dimensional (2d) Ising model on a infinitely long cylinder and study the probabilities $p_i$ to observe a given spin configuration $i$ along a circular section of the cylinder. These probabilities also occur as eigenvalues of reduced density matrices in some Rokhsar-Kivelson wave-functions. We analyze the subleading constant to the Rényi entropy $R_n=1/(1-n) \ln (\sum_i p_i^n)$ and discuss its scaling properties at the critical point. Studying three different microscopic realizations, we provide numerical evidence that it is universal and behaves in a step-like fashion as a function of $n$, with a discontinuity at the Shannon point $n=1$. As a consequence, a field theoretical argument based on the replica trick would fail to give the correct value at this point. We nevertheless compute it numerically with high precision. Two other values of the Rényi parameter are of special interest: $n=1/2$ and $n=\infty$ are related in a simple way to the Affleck-Ludwig boundary entropies associated to free and fixed boundary conditions respectively.

cond-mat.str-el↗

arXiv2009

Shannon and entanglement entropies of one- and two-dimensional critical wave functions

We study the Shannon entropy of the probability distribution resulting from the ground-state wave function of a one-dimensional quantum model. This entropy is related to the entanglement entropy of a Rokhsar-Kivelson-type wave function built from the corresponding two-dimensional classical model. In both critical and massive cases, we observe that it is composed of an extensive part proportional to the length of the system and a subleading universal constant S_0. In c=1 critical systems (Tomonaga-Luttinger liquids), we find that S_0 is a simple function of the boson compactification radius. This finding is based on a field-theoretical analysis of the Dyson-Gaudin gas related to dimer and Calogero-Sutherland models. We also performed numerical demonstrations in the dimer models and the spin-1/2 XXZ chain. In a massive (crystal) phase, S_0 is related to the ground-state degeneracy. We also examine this entropy in the Ising chain in a transverse field as an example showing a c=1/2 critical point.

cond-mat.str-el↗

arXiv2008

Comment on "Regional Versus Global Entanglement in Resonating-Valence-Bond States"

In a recent Letter [Phys. Rev. Lett. 99, 170502 (2007); quant-ph/0703227], Chandran and coworkers study the entanglement properties of valence bond (VB) states. Their main result is that VB states do not contain (or only an insignificant amount of) two-site entanglement, whereas they possess multi-body entanglement. Two examples ("RVB gas and liquid") are given to illustrate this claim, which essentially comes from a lower bound derived for spin correlators in VB states. We show in this Comment that (i) for the "RVB liquid" on the square lattice, the calculations and conclusions of Chandran et al. are incorrect. (ii) A simple analytical calculation gives the exact value of the correlator for the "RVB gas", showing that the bound found by Chandran et al. is tight. (iii) The lower bound for spin correlators in VB states is equivalent to a celebrated result of Anderson dating from more than 50 years ago.

quant-ph↗