arXiv subjects

Fabien Alet

Publications and source records attributed to Fabien Alet.

At least 73 records · Page 4Linked to original sources

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↗

arXiv2008

Correlations and order parameter at a Coulomb-crystal phase transition in a three-dimensional dimer model

The three-dimensional classical dimer model with interactions shows an unexpected continuous phase transition between an ordered dimer crystal and a Coulomb liquid. A detailed analysis of the critical dimer and monomer correlation functions point to a subtle interplay between the fluctuations of the crystal order parameter and the "magnetic" degrees of freedom present in the Coulomb phase. The distribution probability of the crystal order parameter suggests an emerging continuous O(3) symmetry at the critical point.

cond-mat.stat-mech↗

arXiv2008

Comment on "Quantum Monte Carlo scheme for frustrated Heisenberg antiferromagnets"

Quantum Monte Carlo methods are sophisticated numerical techniques for simulating interacting quantum systems. In some cases, however, they suffer from the notorious "sign problem" and become too inefficient to be useful. A recent publication [J. Wojtkiewicz, Phys. Rev. B 75, 174421 (2007)] claims to have solved the sign problem for a certain class of frustrated quantum spin systems through the use of a bipartite valence bond basis. We show in this Comment that the apparent positivity of the path integral is due to a misconception about the resolution of the identity operator in this basis, and that consequently the sign problem remains a severe obstacle for the simulation of frustrated quantum magnets.

cond-mat.str-el↗

arXiv2007

Valence Bond Entanglement Entropy

We introduce for SU(2) quantum spin systems the Valence Bond Entanglement Entropy as a counting of valence bond spin singlets shared by two subsystems. For a large class of antiferromagnetic systems, it can be calculated in all dimensions with Quantum Monte Carlo simulations in the valence bond basis. We show numerically that this quantity displays all features of the von Neumann entanglement entropy for several one-dimensional systems. For two-dimensional Heisenberg models, we find a strict area law for a Valence Bond Solid state and multiplicative logarithmic corrections for the Neel phase.

cond-mat.str-el↗

arXiv2006

Classical dimers with aligning interactions on the square lattice

We present a detailed study of a model of close-packed dimers on the square lattice with an interaction between nearest-neighbor dimers. The interaction favors parallel alignment of dimers, resulting in a low-temperature crystalline phase. With large-scale Monte Carlo and Transfer Matrix calculations, we show that the crystal melts through a Kosterlitz-Thouless phase transition to give rise to a high-temperature critical phase, with algebraic decays of correlations functions with exponents that vary continuously with the temperature. We give a theoretical interpretation of these results by mapping the model to a Coulomb gas, whose coupling constant and associated exponents are calculated numerically with high precision. Introducing monomers is a marginal perturbation at the Kosterlitz-Thouless transition and gives rise to another critical line. We study this line numerically, showing that it is in the Ashkin-Teller universality class, and terminates in a tricritical point at finite temperature and monomer fugacity. In the course of this work, we also derive analytic results relevant to the non-interacting case of dimer coverings, including a Bethe Ansatz (at the free fermion point) analysis, a detailed discussion of the effective height model and a free field analysis of height fluctuations.

cond-mat.stat-mech↗

arXiv2006

Parity law of the singlet-triplet gap in graphitic ribbons

This work explores the possibility to transfer the parity law of the singlet-triplet gap established for square ladders (gapped for even number of legs, gapless for odd number of legs) to fused polyacenic 1-D systems, i.e., graphite ribbons. Qualitative arguments are presented in favor of a gapped character when the number $n\_ω$ of benzene rings along the ribbon width is odd. A series of numerical calculations (quantitative mapping on spin 1/2 chains, renormalized excitonic treatments and Quantum Monte Carlo) confirm the parity law and the gapless character of the ribbon for even $n\_ω$.

cond-mat.str-el↗

arXiv2006

Unconventional continuous phase transition in a three dimensional dimer model

Phase transitions occupy a central role in physics, due both to their experimental ubiquity and their fundamental conceptual importance. The explanation of universality at phase transitions was the great success of the theory formulated by Ginzburg and Landau, and extended through the renormalization group by Wilson. However, recent theoretical suggestions have challenged this point of view in certain situations. In this Letter we report the first large-scale simulations of a three-dimensional model proposed to be a candidate for requiring a description beyond the Landau-Ginzburg-Wilson framework: we study the phase transition from the dimer crystal to the Coulomb phase in the cubic dimer model. Our numerical results strongly indicate that the transition is continuous and are compatible with a tricritical universality class, at variance with previous proposals.

cond-mat.stat-mech↗

arXiv2006

Doping quantum dimer models on the square lattice

A family of models is proposed to describe the motion of holes in a fluctuating quantum dimer background on the square lattice. Following Castelnovo et al. [Ann. Phys. (NY) 318, 316 (2005)], a generalized Rokhsar-Kivelson Hamiltonian at **finite doping** which can be mapped on a **doped** interacting classical dimer model is constructed. A simple physical extension of this model is also considered. Using numerical computations and simple considerations based on the above exact mapping, we determine the phase diagram of the model showing a number of quantum phases typical of a doped Mott insulator. The two-hole correlation function generically exhibits short-range or long-range algebraic correlations in the solid (columnar) and liquid (critical) phases of the model, respectively. Evidence for an extended region of a doped VBS phase exhibiting holon pairing but **no** phase separation is given. In contrast, we show that hole deconfinement occurs in the staggered dimer phase.

cond-mat.str-el↗

arXiv2005

Exotic quantum phases and phase transitions in correlated matter

We present a pedagogical overview of recent theoretical work on unconventional quantum phases and quantum phase transitions in condensed matter systems. Strong correlations between electrons can lead to a breakdown of two traditional paradigms of solid state physics: Landau's theories of Fermi liquids and phase transitions. We discuss two resulting "exotic" states of matter: topological and critical spin liquids. These two quantum phases do not display any long-range order even at zero temperature. In each case, we show how a gauge theory description is useful to describe the new concepts of topological order, fractionalization and deconfinement of excitations which can be present in such spin liquids. We make brief connections, when possible, to experiments in which the corresponding physics can be probed. Finally, we review recent work on deconfined quantum critical points. The tone of these lecture notes is expository: focus is on gaining a physical picture and understanding, with technical details kept to a minimum.

cond-mat.str-el↗

arXiv2005

Interacting classical dimers on the square lattice

We study a model of close-packed dimers on the square lattice with a nearest neighbor interaction between parallel dimers. This model corresponds to the classical limit of quantum dimer models [D.S. Rokhsar and S.A. Kivelson, Phys. Rev. Lett.{\bf 61}, 2376 (1988)]. By means of Monte Carlo and Transfer Matrix calculations, we show that this system undergoes a Kosterlitz-Thouless transition separating a low temperature ordered phase where dimers are aligned in columns from a high temperature critical phase with continuously varying exponents. This is understood by constructing the corresponding Coulomb gas, whose coupling constant is computed numerically. We also discuss doped models and implications on the finite-temperature phase diagram of quantum dimer models.

cond-mat.stat-mech↗

arXiv2005

Generalized Directed Loop Method for Quantum Monte Carlo Simulations

Efficient quantum Monte Carlo update schemes called directed loops have recently been proposed, which improve the efficiency of simulations of quantum lattice models. We propose to generalize the detailed balance equations at the local level during the loop construction by accounting for the matrix elements of the operators associated with open world-line segments. Using linear programming techniques to solve the generalized equations, we look for optimal construction schemes for directed loops. This also allows for an extension of the directed loop scheme to general lattice models, such as high-spin or bosonic models. The resulting algorithms are bounce-free in larger regions of parameter space than the original directed loop algorithm. The generalized directed loop method is applied to the magnetization process of spin chains in order to compare its efficiency to that of previous directed loop schemes. In contrast to general expectations, we find that minimizing bounces alone does not always lead to more efficient algorithms in terms of autocorrelations of physical observables, because of the non-uniqueness of the bounce-free solutions. We therefore propose different general strategies to further minimize autocorrelations, which can be used as supplementary requirements in any directed loop scheme. We show by calculating autocorrelation times for different observables that such strategies indeed lead to improved efficiency; however we find that the optimal strategy depends not only on the model parameters but also on the observable of interest.

cond-mat.str-el↗

arXiv2004

Supersolids versus phase separation in two-dimensional lattice bosons

We study the nature of the ground state of the strongly-coupled two dimensional extended boson Hubbard model on a square lattice. We demonstrate that strong but finite on-site interaction U along with a comparable nearest-neighbor repulsion V result in a thermodynamically stable supersolid ground state just above half-filling, and that the checker-board crystal is unstable for smaller V, and for any V just below half-filling. The interplay between these two interaction energies results in a rich phase diagram which is studied in detail using quantum Monte Carlo methods.

cond-mat.str-el↗

arXiv2004

Global Phase Diagram of the High Tc Cuprates

The high Tc cuprates have a complex phase diagram with many competing phases. We propose a bosonic effective quantum Hamiltonian based on the projected SO(5) model with extended interactions, which can be derived from the microscopic models of the cuprates. The global phase diagram of this model is obtained using mean-field theory and the Quantum Monte Carlo simulation, which is possible because of the absence of the minus sign problem. We show that this single quantum model can account for most salient features observed in the high Tc cuprates, with different families of the cuprates attributed to different traces in the global phase diagram. Experimental consequences are discussed and new theoretical predictions are presented.

cond-mat.supr-con↗

arXiv2004

Quantum Monte Carlo simulations of confined bosonic atoms in optical lattices

We study properties of ultra-cold bosonic atoms in one, two and three dimensional optical lattices by large scale quantum Monte Carlo simulations of the Bose Hubbard model in parabolic confinement potentials. Local phase structures of the atoms are shown to be accessible via a well defined local compressibility, quantifying a global response of the system to a local perturbation. An indicator for the presence of extended Mott plateaux is shown to stem from the shape of the coherent component of the momentum distribution function, amenable to experimental detection. Additional fine structures in the momentum distribution are found to appear unrelated to the local phase structure, disproving previous claims. We discuss limitations of local potential approximations for confined Bose gases, and the absence of quantum criticality and critical slowing down in parabolic confinement potentials, thus accounting for the fast dynamics in establishing phase coherence in current experiments. In contrast, we find that flat confinement potentials allow quantum critical behavior to be observed already on moderately sized optical lattices. Our results furthermore demonstrate, that the experimental detection of the Mott transition would be significantly eased in flat confinement potentials.

cond-mat.stat-mech↗

arXiv2004

Dual Geometric Worm Algorithm for Two-Dimensional Discrete Classical Lattice Models

We present a dual geometrical worm algorithm for two-dimensional Ising models. The existence of such dual algorithms was first pointed out by Prokof'ev and Svistunov \cite{ProkofevClassical}. The algorithm is defined on the dual lattice and is formulated in terms of bond-variables and can therefore be generalized to other two-dimensional models that can be formulated in terms of bond-variables. We also discuss two related algorithms formulated on the direct lattice, applicable in any dimension. These latter algorithms turn out to be less efficient but of considerable intrinsic interest. We show how such algorithms quite generally can be "directed" by minimizing the probability for the worms to erase themselves. Explicit proofs of detailed balance are given for all the algorithms. In terms of computational efficiency the dual geometrical worm algorithm is comparable to well known cluster algorithms such as the Swendsen-Wang and Wolff algorithms, however, it is quite different in structure and allows for a very simple and efficient implementation. The dual algorithm also allows for a very elegant way of calculating the domain wall free energy.

cond-mat.stat-mech↗

arXiv2004

Computational complexity and simulation of rare events of Ising spin glasses

We discuss the computational complexity of random 2D Ising spin glasses, which represent an interesting class of constraint satisfaction problems for black box optimization. Two extremal cases are considered: (1) the +/- J spin glass, and (2) the Gaussian spin glass. We also study a smooth transition between these two extremal cases. The computational complexity of all studied spin glass systems is found to be dominated by rare events of extremely hard spin glass samples. We show that complexity of all studied spin glass systems is closely related to Frechet extremal value distribution. In a hybrid algorithm that combines the hierarchical Bayesian optimization algorithm (hBOA) with a deterministic bit-flip hill climber, the number of steps performed by both the global searcher (hBOA) and the local searcher follow Frechet distributions. Nonetheless, unlike in methods based purely on local search, the parameters of these distributions confirm good scalability of hBOA with local search. We further argue that standard performance measures for optimization algorithms--such as the average number of evaluations until convergence--can be misleading. Finally, our results indicate that for highly multimodal constraint satisfaction problems, such as Ising spin glasses, recombination-based search can provide qualitatively better results than mutation-based search.

cs.NE↗

arXiv2004

The Generic, Incommensurate Transition in the two-dimensional Boson Hubbard Model

The generic transition in the boson Hubbard model, occurring at an incommensurate chemical potential, is studied in the link-current representation using the recently developed directed geometrical worm algorithm. We find clear evidence for a multi-peak structure in the energy distribution for finite lattices, usually indicative of a first order phase transition. However, this multi-peak structure is shown to disappear in the thermodynamic limit revealing that the true phase transition is second order. These findings cast doubts over the conclusion drawn in a number of previous works considering the relevance of disorder at this transition.

cond-mat.str-el↗

arXiv2003

Directed geometrical worm algorithm applied to the quantum rotor model

We discuss the implementation of a directed geometrical worm algorithm for the study of quantum link-current models. In this algorithm Monte Carlo updates are made through the biased reptation of a worm through the lattice. A directed algorithm is an algorithm where, during the construction of the worm, the probability for erasing the immediately preceding part of the worm, when adding a new part,is minimal. We introduce a simple numerical procedure for minimizing this probability. The procedure only depends on appropriately defined local probabilities and should be generally applicable. Furthermore we show how correlation functions, C(r,tau) can be straightforwardly obtained from the probability of a worm to reach a site (r,tau) away from its starting point independent of whether or not a directed version of the algorithm is used. Detailed analytical proofs of the validity of the Monte Carlo algorithms are presented for both the directed and un-directed geometrical worm algorithms. Results for auto-correlation times and Green functions are presented for the quantum rotor model.

cond-mat.str-el↗