arXiv subjects

Lorenzo Piroli

Publications and source records attributed to Lorenzo Piroli.

81 records · Page 5Linked to original sources

arXiv2016

Local correlations in the attractive 1D Bose gas: from Bethe ansatz to the Gross-Pitaevskii equation

We consider the ground-state properties of an extended one-dimensional Bose gas with pointwise attractive interactions. We take the limit where the interaction strength goes to zero as the system size increases at fixed particle density. In this limit the gas exhibits a quantum phase transition. We compute local correlation functions at zero temperature, both at finite and infinite size. We provide analytic formulas for the experimentally relevant one-point functions $g_2$, $g_3$ and analyze their finite-size corrections. Our results are compared to the mean-field approach based on the Gross-Pitaevskii equation which yields the exact results in the infinite system size limit, but not for finite systems.

cond-mat.quant-gas↗

arXiv2016

Exact steady states for quantum quenches in integrable Heisenberg spin chains

The study of quantum quenches in integrable systems has significantly advanced with the introduction of the Quench Action method, a versatile analytical approach to non-equilibrium dynamics. However, its application is limited to those cases where the overlaps between the initial state and the eigenstates of the Hamiltonian governing the time evolution are known exactly. Conversely, in this work we consider physically interesting initial states for which such overlaps are still unknown. In particular, we focus on different classes of product states in spin-$1/2$ and spin-$1$ integrable chains, such as tilted ferromagnets and antiferromagnets. We get around the missing overlaps by following a recent approach based on the knowledge of complete sets of quasi-local charges. This allows us to provide a closed-form analytical characterization of the effective stationary state reached at long times after the quench, through the Bethe ansatz distributions of particles and holes. We compute the asymptotic value of local correlations and check our predictions against numerical data.

cond-mat.stat-mech↗

arXiv2016

Quantum quenches to the attractive one-dimensional Bose gas: exact results

We study quantum quenches to the one-dimensional Bose gas with attractive interactions in the case when the initial state is an ideal one-dimensional Bose condensate. We focus on properties of the stationary state reached at late times after the quench. This displays a finite density of multi-particle bound states, whose rapidity distribution is determined exactly by means of the quench action method. We discuss the relevance of the multi-particle bound states for the physical properties of the system, computing in particular the stationary value of the local pair correlation function $g_2$.

cond-mat.quant-gas↗

arXiv2016

Quantum quenches in the sinh-Gordon model: steady state and one point correlation functions

We consider quantum quenches to the sinh-Gordon integrable quantum field theory from a particular class of initial states. Our analysis includes the case of mass and interaction quenches starting from a non-interacting theory. By means of the recently developed quench action method, we fully characterize the stationary state reached at long times after the quench in terms of the corresponding rapidity distribution. We also provide exact results for the expectation values of arbitrary vertex operators in the post-quench stationary state by proposing a formula based on the analogy with the standard thermodynamic Bethe ansatz. Finally, we comment on the behavior of the post-quench stationary state under the mapping between the sinh-Gordon field theory and the one-dimensional Lieb-Liniger model.

cond-mat.stat-mech↗

arXiv2016

Quasi-local conserved charges and spin transport in spin-$1$ integrable chains

We consider the integrable one-dimensional spin-$1$ chain defined by the Zamolodchikov-Fateev (ZF) Hamiltonian. The latter is parametrized, analogously to the XXZ spin-$1/2$ model, by a continuous anisotropy parameter and at the isotropic point coincides with the well-known spin-$1$ Babujian-Takhtajan Hamiltonian. Following a procedure recently developed for the XXZ model, we explicitly construct a continuous family of quasi-local conserved operators for the periodic spin-$1$ ZF chain. Our construction is valid for a dense set of commensurate values of the anisotropy parameter in the gapless regime where the isotropic point is excluded. Using the Mazur inequality, we show that, as for the XXZ model, these quasi-local charges are enough to prove that the high-temperature spin Drude weight is non-vanishing in the thermodynamic limit, thus establishing ballistic spin transport at high temperature.

cond-mat.stat-mech↗

arXiv2016

Multi-particle bound state formation following a quantum quench to the one-dimensional Bose gas with attractive interactions

We consider quantum quenches from an ideal Bose condensate to the Lieb-Liniger model with arbitrary attractive interaction strength. We focus on the properties of the non-equilibrium steady state reached at late times after the quench. Using recently developed methods based on integrability, we obtain an exact description of the stationary state for a large number of bosons. A distinctive feature of this state is the presence of a hierarchy of multi-particle bound states. We determine the dependence of their densities on interaction strength and obtain an exact expression for the stationary value of the local pair correlation $g_2$. We discuss ramifications of our results for cold atom experiments.

cond-mat.quant-gas↗

arXiv2015

Exact formulas for the form factors of local operators in the Lieb-Liniger model

We present exact formulas for the form factors of local operators in the repulsive Lieb-Liniger model at finite size. These are essential ingredients for both numerical and analytical calculations. From the theory of Algebraic Bethe Ansatz, it is known that the form factors of local operators satisfy a particular type of recursive relations. We show that in some cases these relations can be used directly to derive compact expressions in terms of the determinant of a matrix whose dimension scales linearly with the system size. Our main results are determinant formulas for the form factors of the operators $(Ψ^{\dagger}(0))^2Ψ^2(0)$ and $Ψ^{R}(0)$, for arbitrary integer $R$, where $Ψ$, $Ψ^{\dagger}$ are the usual field operators. From these expressions, we also derive the infinite size limit of the form factors of these local operators in the attractive regime.

cond-mat.stat-mech↗

arXiv2015

Relaxation dynamics of local observables in integrable systems

We show, using the quench action approach [Caux&Essler Phys. Rev. Lett. 110 (2013)], that the whole post-quench time evolution of an integrable system in the thermodynamic limit can be computed with a minimal set of data which are encoded in what we denote the generalized single-particle overlap coefficient $s_0^{Ψ_0}(λ)$. This function can be extracted from the thermodynamically leading part of the overlaps between the eigenstates of the model and the initial state. For a generic global quench the shape of $s_0^{Ψ_0}(λ)$ in the low momentum limit directly gives the exponent for the power law decay to the effective steady state. As an example we compute the time evolution of the static density-density correlation in the interacting Lieb-Liniger gas after a quench from a Bose-Einstein condensate. This shows an approach to equilibrium with power law $t^{-3}$ which turns out to be independent of the post-quench interaction and of the considered observable.

cond-mat.quant-gas↗

arXiv2014

Recursive formulas for the overlaps between Bethe states and product states in XXZ Heisenberg chains

We consider the problem of computing the overlaps between the Bethe states of the XXZ spin-1/2 chain and generic states. We derive recursive formulas for the overlaps between some simple product states and off-shell Bethe states within the framework of the Algebraic Bethe Ansatz. These recursive formulas can be used to prove in a simple and straightforward way the recently-obtained results for the overlaps of the Bethe states with the Néel state, the dimer state, and the \textit{q}-deformed dimer state. However, these recursive formulas are derived for a broader class of states and represent a concrete starting point for the computation of rather general overlaps. Our approach can be easily extended to other one-dimensional Bethe Ansatz integrable models.

cond-mat.stat-mech↗