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arXiv:1809.03688 · Physical review. B./Physical review. B

Quantum critical phenomena in heat transport via a two-state system

Tsuyoshi Yamamoto, Takeo Kato

Published Dec 11, 2018• 6 citations
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Abstract

We present a theoretical study of the quantum critical behavior in heat transport via a two-state system with subohmic reservoirs. We calculate the temperature dependence of the thermal conductance near the quantum phase transition via the continuous-time quantum Monte Carlo method and discuss its critical exponents. We also propose a superconducting circuit to realize the subohmic spin-boson model that can be used to observe quantum critical phenomena.

DOI
10.1103/physrevb.98.245412

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We present a theoretical study of the quantum critical behavior in heat transport via a two-state system with subohmic reservoirs. We calculate the temperature dependence of the thermal conductance near the quantum phase transition via the continuous-time quantum Monte Carlo method and discuss its critical exponents. We also propose a superconducting circuit to realize the subohmic spin-boson model that can be used to observe quantum critical phenomena.
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We investigate the impact of quantum and thermal phase fluctuations on the suppression of superconducting order in two-dimensional systems. Within the two-dimensional quantum XY model in the phase representation, where on-site interaction terms govern quantum phase fluctuations, we perform extensive path-integral quantum Monte Carlo simulations. The resulting temperature-interaction phase diagram establishes the presence of a well-defined critical line ending at a quantum critical point at vanishing temperature with no indication of reentrant behavior. We further demonstrate that the resistance above the critical line reproduces the two expected different critical behaviors. For stronger interactions, above the quantum critical point, the system exhibits a crossover to an insulating regime at low temperatures. Finally, Monte Carlo calculations of current-current correlation functions enable us to extract the frequency-dependent conductivity in both superconducting and normal regimes, revealing a finite-frequency response that we attribute to quantum phase fluctuations.
Understanding the real time dynamics of quantum systems without quasiparticles constitutes an important yet challenging problem. We study the superfluid-insulator quantum-critical point of bosons on a two-dimensional lattice, a system whose excitations cannot be described in a quasiparticle basis. We present detailed quantum Monte Carlo results for two separate lattice realizations: their low-frequency conductivities are found to have the same universal dependence on imaginary frequency and temperature. We then use the structure of the real time dynamics of conformal field theories described by the holographic gauge/gravity duality to make progress on the dicult problem of analytically continuing the Monte Carlo data to real time. Our method yields quantitative and experimentally testable results on the frequency-dependent conductivity near the quantum critical point, and on the spectrum of quasinormal modes in the vicinity of the superfluid-insulator quantum phase transition. Extensions to other observables and universality classes are discussed.
Metallic quantum critical phenomena are believed to play a key role in many strongly correlated materials, including high-temperature superconductors. Theoretically, the problem of quantum criticality in the presence of a Fermi surface has proven to be highly challenging. However, it has recently been realized that many models used to describe such systems are amenable to numerically exact solution by quantum Monte Carlo (QMC) techniques, without suffering from the fermion sign problem. In this review, we examine the status of the understanding of metallic quantum criticality and the recent progress made by QMC simulations. We focus on the cases of spin-density wave and Ising nematic criticality. We describe the results obtained so far and their implications for superconductivity, non-Fermi liquid behavior, and transport near metallic quantum critical points. Some of the outstanding puzzles and future directions are highlighted.
We consider multiple noninteracting quantum mechanical two-level systems coupled to a common bosonic bath and study its quantum phase transition with Monte Carlo simulations using a continuous imaginary time cluster algorithm. The common bath induces an effective ferromagnetic interaction between the otherwise independent two-level systems, which can be quantified by an effective interaction strength. For degenerate energy levels above a critical value of the bath coupling strength $\ensuremath{\alpha}$ all two-level systems freeze into the same state and the critical value ${\ensuremath{\alpha}}_{c}$ decreases asymptotically as 1/N1/N1/N with increasing NNN. For a finite number NNN of two-level systems the quantum phase transition (at zero temperature) is in the same universality class as the single spin-boson model; in the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$ the system shows mean-field critical behavior independent of the power of the spectral function of the bosonic bath. We also study the influence of a spatial separation of the spins in a bath of bosonic modes with linear dispersion relation on the location and characteristics of the phase transition as well as on correlations between the two-level systems.