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arXiv:2307.13889 · Physical Review Research

Critical phase induced by Berry phase and dissipation in a spin chain

Simon Martin, Tarun Grover

Published Dec 20, 2023• 5 citations
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Abstract

Motivated by experiments on spin chains embedded in a metallic bath, as well as closed quantum systems described by long-range interacting Hamiltonians, we study a critical $\mathrm{SU}(N)$ spin chain perturbed by dissipation, or equivalently, after space-time rotation, long-range spatial interactions. The interplay of dissipation and the Wess-Zumino (Berry phase) term results in a rich phase diagram with multiple renormalization-group fixed points. For a range of the exponent that characterizes the dissipative bath, we find a second-order phase transition between the fixed point that describes an isolated critical spin chain and a dissipation-induced-ordered phase. More interestingly, for a different range of the exponent, we find a stable, gapless, nonrelativistic phase of matter whose existence necessarily requires coupling to the dissipative bath. Upon tuning the exponent, we find that the fixed point corresponding to this gapless, stable phase ``annihilates'' the fixed point that describes the transition out of this phase to the ordered phase. We also study a relativistic version of our model, and we identify a new critical point. We discuss the implications of our work for Kondo lattice systems and engineered long-range interacting quantum systems.

DOI
10.1103/physrevresearch.5.043270

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Motivated by experiments on spin chains embedded in a metallic bath, as well as closed quantum systems described by long-range interacting Hamiltonians, we study a critical SU(N)\mathrm{SU}(N)SU(N) spin chain perturbed by dissipation, or equivalently, after space-time rotation, long-range spatial interactions. The interplay of dissipation and the Wess-Zumino (Berry phase) term results in a rich phase diagram with multiple renormalization-group fixed points. For a range of the exponent that characterizes the dissipative bath, we find a second-order phase transition between the fixed point that describes an isolated critical spin chain and a dissipation-induced-ordered phase. More interestingly, for a different range of the exponent, we find a stable, gapless, nonrelativistic phase of matter whose existence necessarily requires coupling to the dissipative bath. Upon tuning the exponent, we find that the fixed point corresponding to this gapless, stable phase ``annihilates'' the fixed point that describes the transition out of this phase to the ordered phase. We also study a relativistic version of our model, and we identify a new critical point. We discuss the implications of our work for Kondo lattice systems and engineered long-range interacting quantum systems.
The phase diagram of the Bose-Fermi Kondo model contains an SU(2)-invariant Kondo-screened phase separated by a continuous quantum phase transition from a Kondo-destroyed local moment phase. We analyze the effect of the Berry phase term of the spin path integral on the quantum critical properties of this quantum impurity model. For a range of the power-law exponent characterizing the spectral density of the dissipative bosonic bath, neglecting the influence of the Berry phase term makes the fixed point Gaussian. For the same range of the spectral density exponent, incorporating the Berry phase term leads instead to an interacting fixed point, for which a quantum to classical mapping breaks down. Some general implications of our results are discussed.
We study the effect of bond dissipation on the one-dimensional antiferromagnetic spin-1/21/21/2 Heisenberg model. In analogy to the spin-Peierls problem, the dissipative bath is described by local harmonic oscillators that modulate the spin exchange coupling, but instead of a single boson frequency we consider a continuous bath spectrum ∝ωs\propto ω^s∝ωs. Using an exact quantum Monte Carlo method for retarded interactions, we show that for s<1s<1s<1 any finite coupling to the bath induces valence-bond-solid order, whereas for s>1s>1s>1 the critical phase of the isolated chain remains stable up to a finite critical coupling. We find that, even in the presence of the gapless bosonic spectrum, the spin-triplet gap remains well defined for any system size, from which we extract a dynamical critical exponent of z=1z=1z=1. We provide evidence for a Berezinskii-Kosterlitz-Thouless quantum phase transition that is governed by the SU(2)1_11​ Wess-Zumino-Witten model. Our results suggest that the critical properties of the dissipative system are the same as for the spin-Peierls model, irrespective of the different interaction range, i.e., power-law vs. exponential decay, of the retarded dimer-dimer interaction, indicating that the spin-Peierls criticality is robust with respect to the bosonic density of states.
The environmental interaction is a fundamental consideration in any controlled quantum system. While an interaction with a dissipative bath can lead to decoherence, it can also provide desirable emergent effects including induced spin-spin correlations. In this Letter, we show that under quite general conditions, a dissipative bosonic bath can induce a long-range ordered phase, without the inclusion of any additional direct spin-spin couplings. Through a quantum-to-classical mapping and classical Monte Carlo simulation, we investigate the T=0T=0T=0 quantum phase transition of an Ising chain embedded in a bosonic bath with Ohmic dissipation. We show that the quantum critical point is continuous, Lorentz invariant with a dynamical critical exponent z=1.07(9)z=1.07(9)z=1.07(9), has a correlation length exponent $\ensuremath{\nu}=0.80(5)$, and anomalous exponent $\ensuremath{\eta}=1.02(6)$, thus the universality class is distinct from the previously studied limiting cases. The implications of our results on experiments in ultracold atomic mixtures and qubit chains in dissipative environments are discussed.
Spin-boson models are simple examples of quantum dissipative systems, but also serve as effective models in quantum magnetism and exhibit nontrivial criticality. Recently, they have been established as a platform to study the nontrivial renormalization-group (RG) scenario of fixed-point annihilation, in which two intermediate-coupling RG fixed points collide and generate an extremely slow RG flow near the collision. For the Bose Kondo model, a single S=1/2S=1/2S=1/2 spin where each spin component couples to an independent bosonic bath with power-law spectrum ∝ωs\propto ω^s∝ωs via dissipation strengths αiα_iαi​, i∈{x,y,z}i\in\{x,y,z\}i∈{x,y,z}, such phenomena occur sequentially for the U(1)-symmetric model at αz=0α_z=0αz​=0 and the SU(2)-symmetric case at αz=αxyα_z = α_{xy}αz​=αxy​, as the bath exponent s<1s<1s<1 is tuned. Here we use an exact wormhole quantum Monte Carlo method for retarded interactions to explore how this nontrivial fixed-point structure affects the phase diagram and phase transitions of the anisotropic model. In particular, we show how fixed-point annihilation within a symmetry-enhanced critical manifold leads to (i) a continuous order-to-order transition beyond the Landau paradigm, (ii) a symmetry-enhanced first-order transition, and (iii) pseudocriticality, which can be tuned into each other via the bath exponent sss. We extract critical exponents at the continuous transition, but also find scaling behavior at the symmetry-enhanced first-order transition, for which the inverse correlation-length exponent is given by the bath exponent sss. Moreover, we provide direct numerical evidence for pseudocritical scaling on both sides of the fixed-point collision, which manifests in an extremely slow drift of the correlation-length exponent. We also study the crossover away from the SU(2)-symmetric case and determine the phase boundary of an extended U(1)-symmetric critical phase.
The SU(2)-symmetric three-component spin-boson model (also Bose-Kondo model) exhibits different behavior of quantum phase and phase transition from its widely studied single-component counterpart. In this paper we proposed and theoretically studied a model of two separated spins coupled to a common bosonic bath. For our SU(2)-symmetric model, the stable fixed point representing the nonclassical phase and an unstable fixed point corresponding to the transition between the strong-coupling and nonclassical phases can be continuously tuned by the distance between the two spins. Thus the fixed-point collision and annihilation (FPCAA) could be achieved by simply changing the distance. We also studied in detail variations of the values of the two fixed points above as the distance is changed. Our work is essential for realization of FPCAA in such systems and paves the way for studying related physics such as deconfined criticality and quasiuniversality.
We explore the physics of a spin-1/2 Heisenberg chain with Kondo interaction, Jk{J}_{k}Jk​, to a two-dimensional electron gas. At weak Jk{J}_{k}Jk​ the problem maps onto a Heisenberg chain locally coupled to a dissipative Ohmic bath. At the decoupled fixed point, the dissipation is a marginally relevant perturbation and drives long-range antiferromagnetic order along the chain. In the dynamical spin structure factor we observe a quadratic low-energy dispersion akin to Landau-damped Goldstone modes. At large Jk{J}_{k}Jk​ Kondo screening dominates, and the spin correlations of the chain inherit the power law of the host metal, akin to a paramagnetic heavy Fermi liquid. In both phases we observe heavy bands near the Fermi energy in the composite-fermion spectral function. Our results, obtained from auxiliary-field quantum Monte Carlo simulations, provide a negative-sign-free realization of a quantum transition between an antiferromagnetic metal and a heavy-fermion metal. We discuss the relevance of our results in the context of scanning tunneling spectroscopy experiments of magnetic adatom chains on metallic surfaces.