arXiv subjects

G. Mussardo

Publications and source records attributed to G. Mussardo.

At least 19 recordsLinked to original sources

arXiv2024

Quantum dynamics of atoms in number-theory-inspired potentials

In this paper we study transitions of atoms between energy levels of several number-theory-inspired atom potentials, under the effect of time-dependent perturbations. First, we simulate in detail the case of a trap whose one-particle spectrum is given by prime numbers. We investigate one-body Rabi oscillations and the excitation lineshape for two resonantly coupled energy levels. We also show that techniques from quantum control are effective in reducing the transition time, compared to the case of a periodic perturbation. Next, we investigate cascades of such transitions. To this end, we pose the following question: can one construct a quantum system where the existence of a continuous resonant cascade is predicted on the validity of a particular statement in number theory? We find that a one-body trap with a log-natural spectrum, parametrically driven with a perturbation of a log-natural frequency, provides such a quantum system. Here, powers of a given natural number will form a ladder of equidistant energy levels; absence of gaps in this ladder is an indication of the validity of the number theory statement in question. Ideas for two more resonance cascade experiments are presented as well: they are designed to illustrate the validity of the Diophantus-Brahmagupta-Fibonacci identity (the set of sums of two squares of integers is closed under multiplication) and the validity of the Goldbach conjecture (every even number is a sum of two primes).

quant-ph↗

arXiv2023

Quantum Integrability vs Experiments: Correlation Functions and Dynamical Structure Factors

Integrable Quantum Field Theories can be solved exactly using bootstrap techniques based on their elastic and factorisable S-matrix. While knowledge of the scattering amplitudes reveals the exact spectrum of particles and their on-shell dynamics, the expression of the matrix elements of the various operators allows the reconstruction of off-shell quantities such as two-point correlation functions with a high level of precision. In this review, we summarise results relevant to the contact point between theory and experiment providing a number of quantities that can be computed theoretically with great accuracy. We concentrate on universal amplitude ratios which can be determined from the measurement of generalised susceptibilities, and dynamical structure factors, which can be accessed experimentally e.g. via inelastic neutron scattering or nuclear magnetic resonance. Besides an overview of the subject and a summary of recent advances, we also present new results regarding generalised susceptibilities in the tricritical Ising universality class.

cond-mat.stat-mech↗

arXiv2022

Variations on vacuum decay: the scaling Ising and tricritical Ising field theories

We study the decay of the false vacuum in the scaling Ising and tricritical Ising field theories using the Truncated Conformal Space Approach and compare the numerical results to theoretical predictions in the thin wall limit. In the Ising case, the results are consistent with previous studies on the quantum spin chain and the $φ^4$ quantum field theory; in particular we confirm that while the theoretical predictions get the dependence of the bubble nucleation rate on the latent heat right, they are off by a model dependent overall coefficient. The tricritical Ising model allows us on the other hand to examine more exotic vacuum degeneracy structures, such as three vacua or two asymmetric vacua, which leads us to study several novel scenarios of false vacuum decay by lifting the vacuum degeneracy using different perturbations.

hep-th↗

arXiv2022

Duality and Form Factors in the Thermally Deformed Two-Dimensional Tricritical Ising Model

The thermal deformation of the critical point action of the 2D tricritical Ising model gives rise to an exact scattering theory with seven massive excitations based on the exceptional $E_7$ Lie algebra. The high and low temperature phases of this model are related by duality. This duality guarantees that the leading and sub-leading magnetisation operators, $σ(x)$ and $σ'(x)$, in either phase are accompanied by associated disorder operators, $μ(x)$ and $μ'(x)$. Working specifically in the high temperature phase, we write down the sets of bootstrap equations for these four operators. For $σ(x)$ and $σ'(x)$, the equations are identical in form and are parameterised by the values of the one-particle form factors of the two lightest $\mathbb{Z}_2$ odd particles. Similarly, the equations for $μ(x)$ and $μ'(x)$ have identical form and are parameterised by two elementary form factors. Using the clustering property, we show that these four sets of solutions are eventually not independent; instead, the parameters of the solutions for $σ(x)/σ'(x)$ are fixed in terms of those for $μ(x)/μ'(x)$. We use the truncated conformal space approach to confirm numerically the derived expressions of the matrix elements as well as the validity of the $Δ$-sum rule as applied to the off-critical correlators. We employ the derived form factors of the order and disorder operators to compute the exact dynamical structure factors of the theory, a set of quantities with a rich spectroscopy which may be directly tested in future inelastic neutron or Raman scattering experiments.

cond-mat.stat-mech↗

arXiv2022

Confinement in the tricritical Ising model

We study the leading and sub-leading magnetic perturbations of the thermal $E_7$ integrable deformation of the tricritical Ising model. In the low-temperature phase, these magnetic perturbations lead to the confinement of the kinks of the model. The resulting meson spectrum can be obtained using the semi-classical quantisation, here extended to include also mesonic excitations composed of two different kinks. An interesting feature of the integrable sub-leading magnetic perturbation of the thermal $E_7$ deformation of the model is the possibility to swap the role of the two operators, i.e. the possibility to consider the model as a thermal perturbation of the integrable $\mathcal{A}_3$ model associated to the sub-leading magnetic deformation. Due to the occurrence of vacuum degeneracy unrelated to spontaneous symmetry breaking in $\mathcal{A}_3$, the confinement pattern shows novel features compared to previously studied models. Interestingly enough, the validity of the semi-classical description in terms of the $\mathcal{A}_3$ endpoint extends well beyond small fields, and therefore the full parameter space of the joint thermal and sub-leading magnetic deformation is well described by a combination of semi-classical approaches. All predictions are verified by comparison to finite volume spectrum resulting from truncated conformal space.

hep-th↗

arXiv2021

$E_8$ Spectra of Quasi-one-dimensional Antiferromagnet BaCo$_2$V$_2$O$_8$ under Transverse Field

We report $^{51}$V nuclear magnetic resonance (NMR) and inelastic neutron scattering (INS) measurements on a quasi-1D antiferromagnet BaCo$_2$V$_2$O$_8$ under transverse field along the [010] direction. The scaling behavior of the spin-lattice relaxation rate above the Néel temperatures unveils a 1D quantum critical point (QCP) at $H_c^{1D}\approx 4.7$ T, which is masked by the 3D magnetic order. With the aid of accurate analytical analysis and numerical calculations, we show that the zone center INS spectrum at $H_c^{1D}$ is precisely described by the pattern of the 1D quantum Ising model in a magnetic field, a class of universality described in terms of the exceptional $E_8$ Lie algebra. These excitations keep to be non-diffusive over a certain field range when the system is away from the 1D QCP. Our results provide an unambiguous experimental realization of the massive $E_8$ phase in the compound, and open new experimental route for exploring the dynamics of quantum integrable systems as well as physics beyond integrability.

cond-mat.str-el↗

arXiv2016

On Truncated Generalized Gibbs Ensembles in the Ising Field Theory

We discuss the implementation of two different truncated Generalized Gibbs Ensembles (GGE) describing the stationary state after a mass quench process in the Ising Field Theory. One truncated GGE is based on the semi-local charges of the model, the other on regularized versions of its ultra-local charges. We test the efficiency of the two different ensembles by comparing their predictions for the stationary state values of the single-particle Green's function $G(x) = \langle ψ^{\dagger}(x) ψ(0) \rangle$ of the complex fermion field $ψ(x)$. We find that both truncated GGEs are able to recover $G(x)$, but for a given number of charges the semi-local version performs better.

cond-mat.stat-mech↗

arXiv2015

Generalized Gibbs Ensembles for Quantum Field Theories

We consider the non-equilibrium dynamics in isolated systems, described by quantum field theories (QFTs). After being prepared in a density matrix that is not an eigenstate of the Hamiltonian, such systems are expected to relax locally to a stationary state. In a presence of local conservation laws, these stationary states are believed to be described by appropriate generalized Gibbs ensembles. Here we demonstrate that in order to obtain a correct description of the stationary state, it is necessary to take into account conservation laws that are not (ultra-)local in the usual sense of QFT, but fulfil a significantly weaker form of locality. We discuss implications of our results for integrable QFTs in one spatial dimension.

cond-mat.quant-gas↗

arXiv2013

Quench Dynamics in Randomly Generated Extended Quantum Models

We analyze the thermalization properties and the validity of the Eigenstate Thermalization Hypothesis in a generic class of quantum Hamiltonians where the quench parameter explicitly breaks a Z_2 symmetry. Natural realizations of such systems are given by random matrices expressed in a block form where the terms responsible for the quench dynamics are the off-diagonal blocks. Our analysis examines both dense and sparse random matrix realizations of the Hamiltonians and the observables. Sparse random matrices may be associated with local quantum Hamiltonians and they show a different spread of the observables on the energy eigenstates with respect to the dense ones. In particular, the numerical data seems to support the existence of rare states, i.e. states where the observables take expectation values which are different compared to the typical ones sampled by the micro-canonical distribution. In the case of sparse random matrices we also extract the finite size behavior of two different time scales associated with the thermalization process.

cond-mat.stat-mech↗

arXiv2010

Local Correlations in the Super Tonks-Girardeau Gas

We study the local correlations in the super Tonks-Girardeau gas, a highly excited, strongly correlated state obtained in quasi one-dimensional Bose gases by tuning the scattering length to large negative values using a confinement-induced resonance. Exploiting a connection with a relativistic field theory, we obtain results for the two-body and three-body local correlators at zero and finite temperature. At zero temperature our result for the three-body correlator agrees with the extension of the results of Cheianov et al. [Phys. Rev. A 73, 051604(R) (2006)], obtained for the ground-state of the repulsive Lieb-Liniger gas, to the super Tonks-Girardeau state. At finite temperature we obtain that the three-body correlator has a weak dependence on the temperature up to the degeneracy temperature. We also find that for temperatures larger than the degeneracy temperature the values of the three-body correlator for the super Tonks-Girardeau gas and the corresponding repulsive Lieb-Liniger gas are rather similar even for relatively small couplings.

cond-mat.quant-gas↗

arXiv2010

1D Lieb-Liniger Bose Gas as Non-Relativistic Limit of the Sinh-Gordon Model

The repulsive Lieb-Liniger model can be obtained as the non-relativistic limit of the Sinh-Gordon model: all physical quantities of the latter model (S-matrix, Lagrangian and operators) can be put in correspondence with those of the former. We use this mapping, together with the Thermodynamical Bethe Ansatz equations and the exact form factors of the Sinh-Gordon model, to set up a compact and general formalism for computing the expectation values of the Lieb-Liniger model both at zero and finite temperature. The computation of one-point correlators is thoroughly detailed and, when possible, compared with known results in the literature.

cond-mat.stat-mech↗

arXiv2010

Energy Level Distribution of Perturbed Conformal Field Theories

We study the energy level spacing of perturbed conformal minimal models in finite volume, considering perturbations of such models that are massive but not necessarily integrable. We compute their spectrum using a renormalization group improved truncated conformal spectrum approach. With this method we are able to study systems where more than 40000 states are kept and where we determine the energies of the lowest several thousand eigenstates with high accuracy. We find, as expected, that the level spacing statistics of integrable perturbed minimal models are Poissonian while the statistics of non-integrable perturbations are GOE-like. However by varying the system size (and so controlling the positioning of the theory between its IR and UV limits) one can induce crossovers between the two statistical distributions.

cond-mat.stat-mech↗

arXiv2010

(3+1) Massive Dirac Fermions with Ultracold Atoms in Optical Lattices

We propose the experimental realization of (3+1) relativistic Dirac fermions using ultracold atoms in a rotating optical lattice or, alternatively, in a synthetic magnetic field. This approach has the advantage to give mass to the Dirac fermions by coupling the ultracold atoms to a Bragg pulse. A dimensional crossover from (3+1) to (2+1) Dirac fermions can be obtained by varying the anisotropy of the lattice. We also discuss under which conditions the interatomic potentials give rise to relativistically invariant interactions among the Dirac fermions.

hep-th↗

arXiv2010

Bethe Ansatz Matrix Elements as Non-Relativistic Limits of Form Factors of Quantum Field Theory

We show that the matrix elements of integrable models computed by the Algebraic Bethe Ansatz can be put in direct correspondence with the Form Factors of integrable relativistic field theories. This happens when the S-matrix of a Bethe Ansatz model can be regarded as a suitable non-relativistic limit of the S-matrix of a field theory, and when there is a well-defined mapping between the Hilbert spaces and operators of the two theories. This correspondence provides an efficient method to compute matrix elements of Bethe Ansatz integrable models, overpassing the technical difficulties of their direct determination. We analyze this correspondence for the simplest example in which it occurs, i.e. the Quantum Non-Linear Schrodinger and the Sinh-Gordon models.

cond-mat.stat-mech↗

arXiv2010

Expectation Values in the Lieb-Liniger Bose Gas

Taking advantage of an exact mapping between a relativistic integrable model and the Lieb-Liniger model we present a novel method to compute expectation values in the Lieb-Liniger Bose gas both at zero and finite temperature. These quantities, relevant in the physics of one-dimensional ultracold Bose gases, are expressed by a series that has a remarkable behavior of convergence. Among other results, we show the computation of the three-body expectation value at finite temperature, a quantity that rules the recombination rate of the Bose gas.

cond-mat.stat-mech↗

arXiv2009

Ultracold Bosons with 3-Body Attractive Interactions in an Optical Lattice

We study the effect of an optical lattice (OL) on the ground-state properties of one-dimensional ultracold bosons with three-body attraction and two-body repulsion, which are described by a cubic-quintic Gross-Pitaevskii equation with a periodic potential. Without the OL and with a vanishing two-body interaction term, soliton solutions of the Townes type are possible only at a critical value of the three-body interaction strength, at which an infinite degeneracy of the ground-state occurs; a repulsive two-body interaction makes such localized solutions unstable. We show that the OL opens a stability window around the critical point when the strength of the periodic potential is above a critical threshold. We also consider the effect of an external parabolic trap, studying how the stability of the solitons depends on matching between minima of the periodic potential and the minimum of the parabolic trap.

cond-mat.stat-mech↗

arXiv2009

Effective potentials and kink spectra in non-integrable perturbed conformal field theories

We analyze the evolution of the effective potential and the particle spectrum of two-parameter families of non-integrable quantum field theories. These theories are defined by deformations of conformal minimal models M_m by using the operators Phi_{1,3}, Phi_{1,2} and Phi_{2,1}. This study extends to all minimal models the analysis previously done for the classes of universality of the Ising, the Tricritical Ising and the RSOS models. We establish the symmetry and the duality properties of the various models also identifying the limiting theories that emerge when m goes to infinity.

hep-th↗

arXiv2008

One-Dimensional Bose Gases with N-Body Attractive Interactions

We study the ground state properties of a one-dimensional Bose gas with N-body attractive contact interactions. By using the explicit form of the bright soliton solution of a generalized nonlinear Schroedinger equation, we compute the chemical potential and the ground state energy. For N=3, a localized soliton wave-function exists only for a critical value of the interaction strength: in this case the ground state has an infinite degeneracy that can be parameterized by the chemical potential. The stabilization of the bright soliton solution by an external harmonic trap is also discussed, and a comparison with the effect of N-body attractive contact interactions in higher dimensions is presented.

cond-mat.stat-mech↗