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Register a new userLieb-Liniger model with exponentially-decaying interactions: a continuous matrix product state study
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The Lieb-Liniger model describes one-dimensional bosons interacting through a repulsive contact potential. In this work, we introduce an extended version of this model by replacing the contact potential with a decaying exponential. Using the recently developed continuous matrix product states techniques, we explore the ground state phase diagram of this model by examining the superfluid and density correlation functions. At weak coupling superfluidity governs the ground state, in a similar way as in the Lieb-Liniger model. However, at strong coupling quasi-crystal and super-Tonks-Girardeau regimes are also found, which are not present in the original Lieb-Liniger case. Therefore the presence of the exponentially-decaying potential leads to a superfluid/super-Tonks-Girardeau/quasi-crystal crossover, when tuning the coupling strength from weak to strong interactions. This corresponds to a Luttinger liquid parameter in the range $K in (0, infty)$; in contrast with the Lieb-Liniger model, where $K in [1, infty)$, and the screened long-range potential, where $K in (0, 1]$.
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The kicked rotor system is a textbook example of how classical and quantum dynamics can drastically differ. The energy of a classical particle confined to a ring and kicked periodically will increase linearly in time whereas in the quantum version the energy saturates after a finite number of kicks. The quantum system undergoes Anderson localization in the angular-momentum space. Conventional wisdom says that in a many-particle system with short-range interactions the localization will be destroyed due to the coupling of widely separated momentum states. Here we provide evidence that for an interacting one-dimensional Bose gas, the Lieb-Linger model, the dynamical localization can persist.
Aiming at studying the emergence of Non-Equilibrium Steady States (NESS) in quantum integrable models by means of an exact analytical method, we focus on the Tonks-Girardeau or hard-core boson limit of the Lieb-Liniger model. We consider the abrupt expansion of a gas from one half to the entire confining box, a prototypical case of inhomogeneous quench, also known as geometric quench. Based on the exact calculation of quench overlaps, we develop an analytical method for the derivation of the NESS by rigorously treating the thermodynamic and large time and distance limit. Our method is based on complex analysis tools for the derivation of the asymptotics of the many-body wavefunction, does not make essential use of the effectively non-interacting character of the hard-core boson gas and is sufficiently robust for generalisation to the genuinely interacting case.
We continue our study of the emergence of Non-Equilibrium Steady States in quantum integrable models focusing on the expansion of a Lieb-Liniger gas for arbitrary repulsive interaction. As a first step towards the derivation of the asymptotics of observables in the thermodynamic and large distance and time limit, we derive an exact multiple integral representation of the time evolved many-body wave-function. Starting from the known but complicated expression for the overlaps of the initial state of a geometric quench, which are derived from the Slavnov formula for scalar products of Bethe states, we eliminate the awkward dependence on the system size and distinguish the Bethe states into convenient sectors. These steps allow us to express the rather impractical sum over Bethe states as a multiple rapidity integral in various alternative forms. Moreover, we examine the singularities of the obtained integrand and calculate the contribution of the multivariable kinematical poles, which is essential information for the derivation of the asymptotics of interest.
We study the Haldane model with nearest-neighbor interactions. This model is physically motivated by the associated ultracold atoms implementation. We show that the topological phase of the interacting model can be characterized by a physically observable winding number. The robustness of this number extends well beyond the topological insulator phase towards attractive and repulsive interactions that are comparable to the kinetic energy scale of the model. We identify and characterize the relevant phases of the model.
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.
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