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Register a new userA Quantum Field-Theoretical Perspective on Scale Anomalies in 1D systems with Three-Body Interactions
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We analyze, from a canonical quantum field theory perspective, the problem of one-dimensional particles with three-body attractive interactions, which was recently shown to exhibit a scale anomaly identical to that observed in two-dimensional systems with two-body interactions. We study in detail the properties of the scattering amplitude including both bound and scattering states, using cutoff and dimensional regularization, and clarify the connection between the scale anomaly derived from thermodynamics to the non-vanishing nonrelativistic trace of the energy-momentum tensor.
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We show that the contributions of three-quasiparticle interactions to normal Fermi systems at low energies and temperatures are suppressed by n_q/n compared to two-body interactions, where n_q is the density of excited or added quasiparticles and n is the ground-state density. For finite Fermi systems, three-quasiparticle contributions are suppressed by the corresponding ratio of particle numbers N_q/N. This is illustrated for polarons in strongly interacting spin-polarized Fermi gases and for valence neutrons in neutron-rich calcium isotopes.
We numerically investigate 1D Bose-Hubbard chains with onsite disorder by means of exact diagonalization. A primary focus of our work is on characterizing Fock-space localization in this model from the single-particle perspective. For this purpose, we compute the one-particle density matrix (OPDM) in many-body eigenstates. We show that the natural orbitals (the eigenstates of the OPDM) are extended in the ergodic phase and real-space localized when one enters into the MBL phase. Furthermore, the distributions of occupations of the natural orbitals can be used as measures of Fock-space localization in the respective basis. Consistent with previous studies, we observe signatures of a transition from the ergodic to the many-body localized (MBL) regime when increasing the disorder strength. We further demonstrate that Fock-space localization, albeit weaker, is also evidently present in the distribution of the physical densities in the MBL regime, both for soft- and hardcore bosons. Moreover, the full distribution of the densities of the physical particles provides a one-particle measure for the detection of the ergodic-MBL transition which could be directly accessed in experiments with ultra-cold gases.
In one spatial dimension, quantum systems with an attractive three-body contact interaction exhibit a scale anomaly. In this work, we examine the few-body sector for up to six particles. We study those systems with a self-consistent, non-perturbative, iterative method, in the subspace of zero total momentum. Exploiting the structure of the contact interaction, the method reduces the complexity of obtaining the wavefunction by three powers of the dimension of the Hilbert space. We present results on the energy, and momentum and spatial structure, as well as Tans contact. We find a Fermi-Fermi crossover interpolating between large, weakly bound trimers and compact, deeply bound trimers: at weak coupling, the behavior is captured by degenerate perturbation theory; at strong coupling, the system is governed by an effective theory of heavy trimers (plus free particles in the case of asymmetric systems). Additionally, we find that there is no trimer-trimer attraction and therefore no six-body bound state.
Traditional anyons in two dimensions have generalized exchange statistics governed by the braid group. By analyzing the topology of configuration space, we discover that an alternate generalization of the symmetric group governs particle exchanges when there are hard-core three-body interactions in one-dimension. We call this new exchange symmetry the traid group and demonstrate that it has abelian and non-abelian representations that are neither bosonic nor fermionic, and which also transform differently under particle exchanges than braid group anyons. We show that generalized exchange statistics occur because, like hard-core two-body interactions in two dimensions, hard-core three-body interactions in one dimension create defects with co-dimension two that make configuration space no longer simply-connected. Ultracold atoms in effectively one-dimensional optical traps provide a possible implementation for this alternate manifestation of anyonic physics.
The approach to thermal equilibrium, or thermalization, in isolated quantum systems is among the most fundamental problems in statistical physics. Recent theoretical studies have revealed that thermalization in isolated quantum systems has several remarkable features, which emerge from quantum entanglement and are quite distinct from those in classical systems. Experimentally, well isolated and highly controllable ultracold quantum gases offer an ideal system to study the nonequilibrium dynamics in isolated quantum systems, triggering intensive recent theoretical endeavors on this fundamental subject. Besides thermalization, many isolated quantum systems show intriguing behavior in relaxation processes, especially prethermalization. Prethermalization occurs when there is a clear separation in relevant time scales and has several different physical origins depending on individual systems. In this review, we overview theoretical approaches to the problems of thermalization and prethermalization.
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