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arXiv:2307.07989 · Physical review. B./Physical review. B

Localization induced by spatially uncorrelated subohmic baths in one dimension

Saptarshi Majumdar, Laura Foini, Thierry Giamarchi, Alberto Rosso

Published Nov 17, 2023• 5 citations
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Abstract

We study an incommensurate XXZ spin chain coupled to a collection of local harmonic baths. At zero temperature, by varying the strength of the coupling to the bath the chain undergoes a quantum phase transition between a Luttinger liquid phase and a spin-density wave (SDW). Our results are consistent with the Berezinskii-Kosterlitz-Thouless (BKT) transition. As opposed to the standard mechanism, the SDW emerges in the absence of the opening of a gap, but it is due to ``fractional excitations'' induced by the bath. We also show, by computing the DC conductivity, that the system is insulating in the presence of a subohmic bath. We interpret this phenomenon as localization induced by the bath \`a la Caldeira and Leggett.

DOI
10.1103/physrevb.108.205138

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We study an incommensurate XXZ spin chain coupled to a collection of local harmonic baths. At zero temperature, by varying the strength of the coupling to the bath the chain undergoes a quantum phase transition between a Luttinger liquid phase and a spin-density wave (SDW). Our results are consistent with the Berezinskii-Kosterlitz-Thouless (BKT) transition. As opposed to the standard mechanism, the SDW emerges in the absence of the opening of a gap, but it is due to ``fractional excitations'' induced by the bath. We also show, by computing the DC conductivity, that the system is insulating in the presence of a subohmic bath. We interpret this phenomenon as localization induced by the bath `a la Caldeira and Leggett.
We study an XXZ spin chain, where each spin is coupled to an independent ohmic bath of harmonic oscillators at zero temperature. Using bosonization and numerical techniques, we show the existence of two phases separated by a Kosterlitz-Thouless transition. At low coupling with the bath, the chain remains in a Luttinger liquid (LL) phase with a reduced but finite spin stiffness, while above a critical coupling, the system is in a dissipative phase characterized by a vanishing spin stiffness. We argue that the transport properties are also inhibited: The LL is a perfect conductor, while the dissipative phase displays finite resistivity. Our results show that the effect of the bath can be interpreted as annealed disorder-inducing signatures of localization.
We study an XXZ spin chain at zero magnetization coupled to a collection of local harmonic baths at zero temperature. We map this system on a (1+1)D(1+1)\mathrm{D}(1+1)D effective field theory using bosonization, where the effect of the bath is taken care of in an exact manner. We provide analytical and numerical evidence of the existence of two phases at zero temperature: a Luttinger liquid (LL) and an antiferromagnetic phase (AFM), separated by a phase transition akin to the Berezinsky--Kosterlitz--Thouless type. While the bath is responsible for the LL-AFM transition for subohmic baths, the LL-AFM transition for superohmic baths is due to the interactions within the spin chain.
We study the ground state phase diagram of a one-dimensional hard-core bosonic model with nearest-neighbor interactions (XXZ model) where every site is coupled Ohmically to an independent but identical reservoir, hereby generalizing spin-boson models to interacting spin-boson systems. We show that a bath-induced Bose liquid phase can occur in the ground state phase diagram away from half filling. This phase is compressible, gapless, and conducting but not superfluid. At half filling, only a Luttinger liquid and a charge density wave are found. The phase transition between them is of Kosterlitz-Thouless type where the Luttinger parameter takes a nonuniversal value. The applied quantum Monte Carlo method can be used for all open bosonic and unfrustrated spin systems, regardless of their dimension, filling factor, and spectrum of the dissipation as long as the quantum system couples to the bath via the density operators.
Recent studies of delocalization-localization transitions in disordered quantum chains have highlighted the role of rare, chain-breaking events that favor localization, in particular for high-energy eigenstates related to many-body localization. In this context, we revisit the random-field XXZ spin-1/2 chain at zero temperature with ferromagnetic interactions, equivalent to interacting fermions or hard-core bosons in a random potential with attractive interactions. We argue that localization in this model can be characterized by chain-breaking events, which are probed by the extreme values of simple local observables, such as the on-site density or the local magnetization, that are readily accessible in both experiments and numerical simulations. Adopting a bosonic language, we study the disorder-induced Berezinskii-Kosterlitz-Thouless (BKT) quantum phase transition from superfluid (SF) to Bose glass (BG), and focus on the strong disorder regime where localization is driven by weak links. Based on high-precision density matrix renormalization group simulations, we numerically show that extreme local densities accurately capture the BKT transition, even for relatively short chains ranging from a few dozen to a hundred sites. We also discuss the SF-BG transition in the weak disorder regime, where finite-size effects pose greater challenges. Overall, our work seeks to establish a solid foundation for using extreme statistics of local observables, such as density, to probe delocalization-localization transitions in disordered quantum chains, both in the ground state and at high energy.
We consider the interacting helical liquid system at the one-dimensional edge of a two-dimensional topological insulator, coupled to an external magnetic field and s-wave superconductor and map it to an XYZ spin chain system. This model undergoes quantum Berezinskii–Kosterlitz–Thouless (BKT) transition with two limiting conditions. We derive the renormalization group (RG) equations explicitly and also present the flow lines behavior. We also present the behavior of RG flow lines based on the exact solution. We observe that the physics of Majorana fermion zero modes and the gaped Ising-ferromagnetic phase, which appears in a different context. We observe that the evidence of gapless helical Luttinger liquid phase as a common non-topological quantum phase for both quantum BKT transitions. We explain analytically and physically that there is no Majorana-Ising transition. In the presence of chemical potential, the system shows the commensurate to incommensurate transition.
We investigate a one dimensional quantum fluid coupled to a dissipative bath. The quantum fluid is captured by the canonical Luttinger liquid; the bath is given by the model of Caldeira and Leggett, i.e. a tower of oscillators coupled linearly to the fluid density, ρρρ. The bath can be integrated out exactly, producing an effective interaction for the fluid that is nonlocal in time; we argue that the form corresponding to Ohmic dissipation is generic. Compared to previous works, we compute correlation functions for this minimal model without approximation, including at finite temperature T>0T>0T>0. From these and a Kubo calculation, we conclude that arbitrary dissipation destroys the perfect conductivity of the Luttinger liquid via Zeno localization, even in the absence of a spatial potential; from RG analysis of harmonic terms, we also find that the open Luttinger liquid is significantly more prone to localization by such potentials, in contrast to the usual intuition that baths make systems less localized.