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arXiv:2207.13782 · Physical review. B./Physical review. B

First-order transitions in spin chains coupled to quantum baths

C. A. Perroni, ANTONIO DE CANDIA, V. Cataudella, Rosario Fazio, G. De Filippis

Published Mar 10, 2023• 6 citations
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Abstract

We show that tailoring the dissipative environment allows us to change the features of continuous quantum phase transitions and even induce first-order transitions in ferromagnetic spin chains. In particular, using a numerically exact quantum Monte Carlo method for the paradigmatic Ising chain of one-half spins in a transverse magnetic field, we find that spin couplings to local quantum boson baths (in the Ohmic regime) can drive the transition from the second to the first order even for a low dissipation strength. Moreover, using a variational mean-field approach for the treatment of spin-spin and spin-boson interactions, we point out that phase discontinuities are ascribable to a dissipation-induced effective magnetic field which is intrinsically related to the bath quantum fluctuations and vanishes for classical baths. The effective field is able to switch the sign of the magnetization along the direction of spin-spin interactions. The results can be potentially tested in recent quantum simulators and are relevant for quantum sensing since the spin system could not only detect the properties of nonclassical baths, but also the effects of weak magnetic fields.

DOI
10.1103/physrevb.107.l100302

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We show that tailoring the dissipative environment allows us to change the features of continuous quantum phase transitions and even induce first-order transitions in ferromagnetic spin chains. In particular, using a numerically exact quantum Monte Carlo method for the paradigmatic Ising chain of one-half spins in a transverse magnetic field, we find that spin couplings to local quantum boson baths (in the Ohmic regime) can drive the transition from the second to the first order even for a low dissipation strength. Moreover, using a variational mean-field approach for the treatment of spin-spin and spin-boson interactions, we point out that phase discontinuities are ascribable to a dissipation-induced effective magnetic field which is intrinsically related to the bath quantum fluctuations and vanishes for classical baths. The effective field is able to switch the sign of the magnetization along the direction of spin-spin interactions. The results can be potentially tested in recent quantum simulators and are relevant for quantum sensing since the spin system could not only detect the properties of nonclassical baths, but also the effects of weak magnetic fields.
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.
We study the zero-temperature static properties of dissipative ensembles of quantum Ising spins arranged on periodic one-dimensional finite clusters and on an infinite chain. The spins interact ferro-magnetically with nearest-neighbor pure and random couplings. They are subject to a transverse field and coupled to an Ohmic bath of quantum harmonic oscillators. We analyze the coupled system using Monte Carlo simulations of the classical two-dimensional counterpart model. The coupling to the bath enhances the extent of the ordered phase, as found in mean-field spin glasses. In the case of finite clusters, we show that a generalization of the Caldeira-Leggett localization transition exists. In the case of the infinite random chain, we study the effect of dissipation on the transition and the Griffiths phase.
We study the zero-temperature critical behavior of dissipative quantum Ising spin chains of finite and infinite length. The spins interact with either constant or random nearest-neighbor ferro-magnetic couplings. They are also subject to a transverse field and coupled to an Ohmic bath of quantum harmonic oscillators. We analyze the coupled system performing Monte Carlo simulations on a classical two-dimensional counterpart model. We find that the coupling to the bath enhances the extent of the ordered phase, as it is known for mean-field spin-glass models. In the case of finite chains we show that a generalization of the Caldeira-Leggett localization transition exists.
Dissipative processes can drive different magnetic orders in quantum spin chains. Using a nonperturbative analytic mapping framework, we systematically show how to structure different magnetic orders in spin systems by controlling the locality of the attached baths. Our mapping approach reveals analytically the impact of spin-bath couplings, leading to the suppression of spin splittings, bath dressing and mixing of spin-spin interactions, and emergence of nonlocal ferromagnetic interactions between spins coupled to the same bath, which become long ranged for a global bath. Our general mapping method can be readily applied to a variety of spin models: we demonstrate (i) a bath-induced transition from antiferromagnetic (AFM) to ferromagnetic ordering in a Heisenberg spin chain, (ii) AFM to extended Neel phase ordering within a transverse-field Ising chain with pairwise couplings to baths, and (iii) a quantum phase transition in the fully connected Ising model. Our method is nonperturbative in the system-bath coupling. It holds for a variety of non-Markovian baths and it can be readily applied towards studying bath-engineered phases in frustrated or topological materials.
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.
The effectiveness of the variational approach \`a la Feynman is proved in the spin-boson model, i.e., the simplest realization of the Caldeira-Leggett model able to reveal the quantum phase transition from delocalized to localized states and the quantum dissipation and decoherence effects induced by a heat bath. After exactly eliminating the bath degrees of freedom, we propose a trial, nonlocal in time, interaction between the spin and itself simulating the coupling of the two-level system with the bosonic bath. It stems from a Hamiltonian where the spin is linearly coupled to a finite number of harmonic oscillators whose frequencies and coupling strengths are variationally determined. We show that a very limited number of these fictitious modes is enough to get a remarkable agreement, up to very low temperatures, with the data obtained by using an approximation-free Monte Carlo approach, predicting (1) in the Ohmic regime, a Berezinski-Thouless-Kosterlitz quantum phase transition exhibiting the typical universal jump at the critical value; and (2) in the sub-Ohmic regime ($s\ensuremath{\le}0.5$), mean-field quantum phase transitions, with logarithmic corrections for s=0.5s=0.5s=0.5.