arXiv subjects

Giuseppe Mussardo

Publications and source records attributed to Giuseppe Mussardo.

At least 55 records · Page 3Linked to original sources

arXiv2014

Boundary State in an Integrable Quantum Field Theory Out of Equilibrium

We study a quantum quench of the mass and the interaction in the Sinh-Gordon model starting from a large initial mass and zero initial coupling. Our focus is on the determination of the expansion of the initial state in terms of post-quench excitations. We argue that the large energy profile of the involved excitations can be relevant for the late time behaviour of the system and common regularization schemes are unreliable. We therefore proceed in determining the initial state by first principles expanding it in a systematic and controllable fashion on the basis of the asymptotic states. Our results show that, for the special limit of pre-quench parameters we consider, it assumes a squeezed state form that has been shown to evolve so as to exhibit the equilibrium behaviour predicted by the Generalized Gibbs Ensemble.

cond-mat.stat-mech↗

arXiv2013

Expectation Values of Local Fields in an Integrable Theory after a Quantum Quench

The expectation values of local fields of any interacting quantum theory after a quench process are key quantities for matching theoretical and experimental results. For quantum integrable field theories, we argue that they can be obtained by a generalization of the Leclair-Mussardo formula and a Bethe Ansatz result of Caux and Konik. Specializing to the Sinh-Gordon model and taking the non-relativistic limit, one can recover the results of Kormos et al. for the Lieb-Liniger model.

cond-mat.stat-mech↗

arXiv2013

Infinite-time Average of Local Fields in an Integrable Quantum Field Theory after a Quantum Quench

The infinite-time average of the expectation values of local fields of any interacting quantum theory after a global quench process are key quantities for matching theoretical and experimental results. For quantum integrable field theories, we show that they can be obtained by an ensemble average that employs a particular limit of the Form Factors of local fields and quantities extracted by the Generalized Bethe Ansatz.

cond-mat.stat-mech↗

arXiv2013

Statistical Mechanics of an Ideal Gas of Non-Abelian Anyons

We study the thermodynamical properties of an ideal gas of non-Abelian Chern-Simons particles and we compute the second virial coefficient, considering the effect of general soft-core boundary conditions for the two-body wavefunction at zero distance. The behaviour of the second virial coefficient is studied as a function of the Chern-Simons coupling, the isospin quantum number and the hard-coreness parameters. Expressions for the main thermodynamical quantities at the lower order of the virial expansion are also obtained: we find that at this order the relation between the internal energy and the pressure is the same found (exactly) for 2D Bose and Fermi ideal gases. A discussion of the comparison of obtained findings with available results in literature for systems of hard-core non-Abelian Chern-Simons particles is also supplied.

hep-th↗

arXiv2012

Zamolodchikov-Faddeev Algebra and Quantum Quenches in Integrable Field Theories

We analyze quantum quenches in integrable models and in particular the determination of the initial state in the basis of eigenstates of the post-quench hamiltonian. This leads us to consider the set of transformations of creation and annihilation operators that respect the Zamolodchikov-Faddeev algebra satisfied by integrable models. We establish that the Bogoliubov transformations hold only in the case of quantum quenches in free theories. In the most general case of interacting theories, we identify two classes of transformations. The first class induces a change in the S-matrix of the theory but not of its ground state, whereas the second class results in a "dressing" of the operators. As examples of our approach we consider the transformations associated with a change of the interaction in the Sinh-Gordon and the Lieb-Liniger model.

cond-mat.stat-mech↗

arXiv2012

Statistical Interparticle Potential of an Ideal Gas of Non-Abelian Anyons

We determine and study the statistical interparticle potential of an ideal system of non-Abelian Chern-Simons (NACS) particles, comparing our results with the corresponding results of an ideal gas of Abelian anyons. In the Abelian case, the statistical potential depends on the statistical parameter and it has a "quasi-bosonic" behaviour for statistical parameter in the range (0,1/2) (non-monotonic with a minimum) and a "quasi-fermionic" behaviour for statistical parameter in the range (1/2,1) (monotonically decreasing without a minimum). In the non-Abelian case the behavior of the statistical potential depends on the Chern- Simons coupling and the isospin quantum number: as a function of these two parameters, a phase diagram with quasi-bosonic, quasi-fermionic and bosonic-like regions is obtained and investigated. Finally, using the obtained expression for the statistical potential, we compute the second virial coefficient of the NACS gas, which correctly reproduces the results available in literature.

cond-mat.quant-gas↗

arXiv2010

Integrability, Non-integrability and confinement

We discuss the main features of quantum integrable models taking the classes of universality of the Ising model and the repulsive Lieb-Liniger model as paradigmatic examples. We address the breaking of integrability by means of two approaches, the Form Factor Perturbation Theory and semiclassical methods. Each of them has its own advantage. Using the first approach, one can relate the confinement phenomena of topological excitations to the semi-locality of the operator which breaks integrability. Using the second approach, one can control the bound states which arise in each phase of the theory and predict that their number cannot be more than two.

cond-mat.stat-mech↗

arXiv2010

Long time dynamics following a quench in an integrable quantum spin chain: local versus non-local operators and effective thermal behavior

We study the dynamics of the quantum Ising chain following a zero-temperature quench of the transverse field strength. Focusing on the behavior of two-point spin correlation functions, we show that the correlators of the order parameter display an effective asymptotic thermal behavior, i.e., they decay exponentially to zero, with a phase coherence rate and a correlation length dictated by the equilibrium law with an effective temperature set by the energy of the initial state. On the contrary, the two-point correlation functions of the transverse magnetization or the density-of-kinks operator decay as a power-law and do not exhibit thermal behavior. We argue that the different behavior is linked to the locality of the corresponding operator with respect to the quasi-particles of the model: non-local operators, such as the order parameter, behave thermally, while local ones do not. We study which features of the two-point correlators are a consequence of the integrability of the model by analizing their robustness with respect to a sufficiently strong integrability-breaking term.

cond-mat.stat-mech↗

arXiv2010

Topological Quantum Gate Construction by Iterative Pseudogroup Hashing

We describe the hashing technique to obtain a fast approximation of a target quantum gate in the unitary group SU(2) represented by a product of the elements of a universal basis. The hashing exploits the structure of the icosahedral group [or other finite subgroups of SU(2)] and its pseudogroup approximations to reduce the search within a small number of elements. One of the main advantages of the pseudogroup hashing is the possibility to iterate to obtain more accurate representations of the targets in the spirit of the renormalization group approach. We describe the iterative pseudogroup hashing algorithm using the universal basis given by the braidings of Fibonacci anyons. The analysis of the efficiency of the iterations based on the random matrix theory indicates that the runtime and the braid length scale poly-logarithmically with the final error, comparing favorably to the Solovay-Kitaev algorithm.

quant-ph↗

arXiv2010

Quantum Quenches in Integrable Field Theories

We study the non equilibrium time evolution of an integrable field theory in 1+1 dimensions after a sudden variation of a global parameter of the Hamiltonian. For a class of quenches defined in the text, we compute the long times limit of the one point function of a local operator as a series of form factors. Even if some subtleties force us to handle this result with care, there is a strong evidence that for long times the expectation value of any local operator can be described by a generalized Gibbs ensemble with a different effective temperature for each eigenmode.

cond-mat.stat-mech↗

arXiv2010

Quantum hashing with the icosahedral group

We study an efficient algorithm to hash any single qubit gate (or unitary matrix) into a braid of Fibonacci anyons represented by a product of icosahedral group elements. By representing the group elements by braid segments of different lengths, we introduce a series of pseudo-groups. Joining these braid segments in a renormalization group fashion, we obtain a Gaussian unitary ensemble of random-matrix representations of braids. With braids of length O[log(1/epsilon)], we can approximate all SU(2) matrices to an average error epsilon with a cost of O[log(1/epsilon)] in time. The algorithm is applicable to generic quantum compiling.

quant-ph↗

arXiv2009

Effective thermal dynamics following a quantum quench in a spin chain

We study the nonequilibrium dynamics of the Quantum Ising Model following an abrupt quench of the transverse field. We focus on the on-site autocorrelation function of the order parameter, and extract the phase coherence time $τ^ϕ_Q$ from its asymptotic behavior. We show that the initial state determines $τ^ϕ_Q$ only through an effective temperature set by its energy and the final Hamiltonian. Moreover, we observe that the dependence of $τ^ϕ_Q$ on the effective temperature fairly agrees with that obtained in thermal equilibrium as a function of the equilibrium temperature.

cond-mat.stat-mech↗

arXiv2008

The particle spectrum of the Tricritical Ising Model with spin reversal symmetric perturbations

We analyze the evolution of the particle spectrum of the Tricritical Ising Model by varying the couplings of the energy and vacancy density fields. The particle content changes from the spectrum of a supersymmetric theory (either of an exact or a spontaneously broken supersymmetric theory) to the spectrum of seven particles related to the underlying E_7 structure. In the low temperature phase some of these excitations are topologically charged particles that are stable under an arbitrary variation of the parameters. The high and low temperature phases of the model are related by duality. In some regions of the two couplings there are also present false vacua and sequences of bound states. In order to study the non-integrable features of this model we employ the Form Factor Perturbation Theory and the Truncated Conformal Space Approach.

hep-th↗

arXiv2008

Analytic properties of the free energy: the tricritical Ising model

We investigate the tricritical Ising model in complex magnetic field in order to characterize the analytic structure of its free energy. By supplementing analytic methods with the truncation of conformal space technique we obtain nonperturbative data even if the field theories we consider are not integrable. The existence of edge singularities analogous to the Lee-Yang points in the Ising field theory is confirmed. A surprising result, due to the conformal dimensions of the operators involved, is the appearance of two branching points which seems appealing to identify with a pair of complex conjugate spinodal singularities.

hep-th↗

arXiv2007

Kink Confinement and Supersymmetry

We analyze non-integrable deformations of two-dimensional N=1 supersymmetric quantum field theories with kink excitations. As example, we consider the multi-frequency Super Sine Gordon model. At weak coupling, this model is robust with respect to kink confinement phenomena, in contrast to the purely bosonic case. If we vary the coupling, the model presents a sequence of phase transitions, where pairs of kinks disappear from the spectrum. The phase transitions fall into two classes: the first presents the critical behaviors of the Tricritical Ising model, the second instead those of the gaussian model. In the first case, close to the critical point, the model has metastable vacua, with a spontaneously supersymmetry breaking. When the life-time of the metastable vacua is sufficiently long, the role of goldstino is given by the massless Majorana fermion of the Ising model. On the contrary, supersymmetry remains exact in the phase transition of the second type.

hep-th↗

arXiv2007

Kinks and Particles in Non-integrable Quantum Field Theories

In this talk we discuss an elementary derivation of the semi-classical spectrum of neutral particles in two field theories with kink excitations. We also show that, in the non-integrable cases, each vacuum state cannot generically support more than two stable particles, since all other neutral exitations are resonances, which will eventually decay.

hep-th↗

arXiv2006

Neutral Bound States in Kink-like Theories

In this paper we present an elementary derivation of the semi-classical spectrum of neutral particles in a field theory with kink excitations. In the non-integrable cases, we show that each vacuum state cannot generically support more than two stable particles, since all other neutral exitations are resonances, which will eventually decay. A phase space estimate of these decay rates is also given. This shows that there may be a window of values of the coupling constant where a particle with higher mass is more stable than the one with lower mass. We also discuss the crossing symmetry properties of the semiclassical form factors and the possibility of extracting the elastic part of the kink $S$-matrix below their inelastic threshold. We present the analysis of theories with symmetric and asymmetric wells, as well as of those with symmetric or asymmetric kinks. Illustrative examples of such theories are provided, among others, by the Tricritical Ising Ising, the Double Sine Gordon model and by a class of potentials recently introduced by Bazeira et al.

hep-th↗

arXiv2001

On the Finite Temperature Formalism in Integrable Quantum Field Theories

Two different theoretical formulations of the finite temperature effects have been recently proposed for integrable field theories. In order to decide which of them is the correct one, we perform for a particular model an explicit check of their predictions for the one-point function of the trace of the stress-energy tensor, a quantity which can be independently determined by the Thermodynamical Bethe Ansatz.

hep-th↗