Lieb-Liniger model with exponentially-decaying interactions: a continuous matrix product state study

Abstract

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 $K\in (0,1]$.

10 pages, 8 figures

References in corpus (19)

• Many-Body Physics with Ultracold Gases
• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Strongly correlated 2D quantum phases with cold polar molecules: controlling the shape of the interaction potential
• Strong dipolar effects in a quantum ferrofluid
• From density-matrix renormalization group to matrix product states
• Bosonizing one-dimensional cold atomic gases
• Scaling of entanglement support for Matrix Product States
• Continuous Matrix Product States for Quantum Fields
• Quantum phase transition in a two-dimensional system of dipoles
• Wilson Fermions and Axion Electrodynamics in Optical Lattices
• Cold atom simulation of interacting relativistic quantum field theories
• Wigner crystal physics in quantum wires
• Matrix product ansatz for Fermi fields in one dimension
• Evidence of Luttinger liquid behavior in one-dimensional dipolar quantum gases
• 1D Quantum Liquids with Power-Law Interactions: a Luttinger Staircase with Polar Molecules
• Interacting bosons in one dimension and Luttinger liquid theory
• Super-Tonks-Girardeau regime in trapped one-dimensional dipolar gases
• Continuous matrix product states for coupled fields: Application to Luttinger Liquids and quantum simulators

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• Variational Neural-Network Ansatz for Continuum Quantum Field Theory
• Variational optimization of continuous matrix product states
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• Spatial entanglement entropy in the ground state of the Lieb-Liniger model
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• Density-Matrix Renormalization Group for Continuous Quantum Systems
• Magic entanglement renormalization for quantum fields
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• Entanglement renormalization for gauge invariant quantum fields
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• A Bayesian Mark Interaction Model for Analysis of Tumor Pathology Images
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• Kac-Moody symmetries in one-dimensional bosonic systems
• Continuous matrix product operators for quantum fields