arXiv subjects

Vincent Pasquier

Publications and source records attributed to Vincent Pasquier.

At least 37 records · Page 2Linked to original sources

arXiv2013

Graphical Calculus for the Double Affine Q-Dependent Braid Group

We define a double affine $Q$-dependent braid group. This group is constructed by appending to the braid group a set of operators $Q_i$, before extending it to an affine $Q$-dependent braid group. We show specifically that the elliptic braid group and the double affine Hecke algebra (DAHA) can be obtained as quotient groups. Complementing this we present a pictorial representation of the double affine $Q$-dependent braid group based on ribbons living in a toroid. We show that in this pictorial representation we can fully describe any DAHA. Specifically, we graphically describe the parameter $q$ upon which this algebra is dependent and show that in this particular representation $q$ corresponds to a twist in the ribbon.

math-ph↗

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

Conformal blocks in Virasoro and W theories: duality and the Calogero-Sutherland model

We study the properties of the conformal blocks of the conformal field theories with Virasoro or W-extended symmetry. When the conformal blocks contain only second-order degenerate fields, the conformal blocks obey second order differential equations and they can be interpreted as ground-state wave functions of a trigonometric Calogero-Sutherland Hamiltonian with non-trivial braiding properties. A generalized duality property relates the two types of second order degenerate fields. By studying this duality we found that the excited states of the Calogero-Sutherland Hamiltonian are characterized by two partitions, or in the case of WA_{k-1} theories by k partitions. By extending the conformal field theories under consideration by a u(1) field, we find that we can put in correspondence the states in the Hilbert state of the extended CFT with the excited non-polynomial eigenstates of the Calogero-Sutherland Hamiltonian. When the action of the Calogero-Sutherland integrals of motion is translated on the Hilbert space, they become identical to the integrals of motion recently discovered by Alba, Fateev, Litvinov and Tarnopolsky in Liouville theory in the context of the AGT conjecture. Upon bosonisation, these integrals of motion can be expressed as a sum of two, or in general k, bosonic Calogero-Sutherland Hamiltonian coupled by an interaction term with a triangular structure. For special values of the coupling constant, the conformal blocks can be expressed in terms of Jack polynomials with pairing properties, and they give electron wave functions for special Fractional Quantum Hall states

hep-th↗

arXiv2011

Anti de Sitter quantum field theory and a new class of hypergeometric identities

We use Anti-de Sitter quantum field theory to prove a new class of identities between hypergeometric functions related to the Källén-Lehmann representation of products of two Anti-de Sitter two-point functions. A rich mathematical structure emerges. We apply our results to study the decay of unstable Anti-de Sitter particles. The total amplitude is in this case finite and Anti-de Sitter invariant.

hep-th↗

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↗

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↗

arXiv2009

Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension

We study the generic scaling properties of the mutual information between two disjoint intervals, in a class of one-dimensional quantum critical systems described by the c=1 bosonic field theory. A numerical analysis of a spin-chain model reveals that the mutual information is scale-invariant and depends directly on the boson radius. We interpret the results in terms of correlation functions of branch-point twist fields. The present study provides a new way to determine the boson radius, and furthermore demonstrates the power of the mutual information to extract more refined information of conformal field theory than the central charge.

cond-mat.stat-mech↗

arXiv2009

Triangular invariants, three-point functions and particle stability on the de Sitter universe

We study a class of three-point functions on the de Sitter universe and on the asymptotic cone. A blending of geometrical ideas and analytic methods is used to compute some remarkable integrals, on the basis of a generalized star-triangle identity living on the cone and on the complex de Sitter manifold. We discuss an application of the general results to the study of the stability of scalar particles on the Sitter universe.

hep-th↗

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↗

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

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↗

arXiv2005

Stability properties of some perfect fluid cosmological models

Flat FRW perfect fluid cosmologies can be reproduced as particular solutions of suitable field theoretical models. Here we investigate the stability of perfect fluid model trajectories with respect to sets of trajectories of the corresponding field models having generic initial conditions. It is shown that the trajectories of barotropic perfect fluid models and those of the Chaplygin gas model are stable. The total probability to reach the Chaplygin gas regime early enough to achieve a matter dominated stage having a realistic duration is calculated for a scalar field model assuming a natural measure in the space of initial conditions taken near a cosmological singularity. An example is presented of a two-fluid cosmological model where the stability is partially absent.

astro-ph↗

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

Quantum dimer model with Z_2 liquid ground-state: interpolation between cylinder and disk topologies and toy model for a topological quantum-bit

We consider a quantum dimer model (QDM) on the kagome lattice which was introduced recently [Phys. Rev. Lett. 89, 137202 (2002)]. It realizes a Z_2 liquid phase and its spectrum was obtained exactly. It displays a topological degeneracy when the lattice has a non-trivial geometry (cylinder, torus, etc). We discuss and solve two extensions of the model where perturbations along lines are introduced: first the introduction of a potential energy term repelling (or attracting) the dimers along a line is added, second a perturbation allowing to create, move or destroy monomers. For each of these perturbations we show that there exists a critical value above which, in the thermodynamic limit, the degeneracy of the ground-state is lifted from 2 (on a cylinder) to 1. In both cases the exact value of the gap between the first two levels is obtained by a mapping to an Ising chain in transverse field. This model provides an example of solvable Hamiltonian for a topological quantum bit where the two perturbations act as a diagonal and a transverse operator in the two-dimensional subspace. We discuss how crossing the transitions may be used in the manipulation of the quantum bit to optimize simultaneously the frequency of operation and the losses due to decoherence.

cond-mat.str-el↗

arXiv2004

Non-commutative field theory approach to two-dimensional vortex liquid system

We investigate the non-commutative (NC) field theory approach to the vortex liquid system restricted to the lowest Landau level (LLL) approximation. NC field theory effectively takes care of the phase space reduction of the LLL physics in a $\star$-product form and introduces a new gauge invariant form of a quartic potential of the order parameter in the Ginzburg-Landau (GL) free energy. This new quartic interaction coupling term has a non-trivial equivalence relation with that obtained by Brézin, Nelson and Thiaville in the usual GL framework. The consequence of the equivalence is discussed.

cond-mat.supr-con↗

arXiv2003

Interaction between static holes in a quantum dimer model on the kagome lattice

A quantum dimer model (QDM) on the kagome lattice with an extensive ground-state entropy was recently introduced [Phys. Rev. B 67, 214413 (2003)]. The ground-state energy of this QDM in presence of one and two static holes is investigated by means of exact diagonalizations on lattices containing up to 144 kagome sites. The interaction energy between the holes (at distances up to 7 lattice spacings) is evaluated and the results show no indication of confinement at large hole separations.

cond-mat.str-el↗

arXiv2003

Quantum dimer model with extensive ground-state entropy on the kagome lattice

We introduce a quantum dimer model on the kagome lattice with kinetic terms allowing from 3 to 6 dimers to resonate around hexagons. Unlike models studied previously, the different resonance loops appears with different signs (given by the parity of the number of dimers involved). These signs naturally appear when performing the lowest-order overlap expansion (Rokhsar and Kivelson 1988) of the Heisenberg model. We demonstrate that the quantum dimer model has an extensive zero-temperature entropy and has very short-range dimer-dimer correlations. We discuss the possible relevance of this new kind of quantum dimer liquid to the physics of the spin-1/2 Heisenberg model on the kagome lattice.

cond-mat.str-el↗