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arXiv:1312.5182 · Physical Review X

Perturbative Field-Theoretical Renormalization Group Approach to Driven-Dissipative Bose-Einstein Criticality

Uwe Claus Täuber, Sebastian Diehl

Published Apr 16, 2014• 71 citations
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Abstract

Fundamental understanding of nonequilibrium phase transitions in quantum many-body systems is still in its infancy but is urgently needed given the recent surge in exploration of light-matter interactions in a variety of quantum systems. A field-theoretical renormalization group study of a light-driven, dissipative model system of bosons contributes an important piece.

DOI
10.1103/physrevx.4.021010

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Fundamental understanding of nonequilibrium phase transitions in quantum many-body systems is still in its infancy but is urgently needed given the recent surge in exploration of light-matter interactions in a variety of quantum systems. A field-theoretical renormalization group study of a light-driven, dissipative model system of bosons contributes an important piece.
Driven-dissipative quantum many-body systems, i.e., many-particle systems where quantum coherent dynamics and dissipative effects occur on the same footing, can constitute a promising platform to initiate a systematic classification of quantum dynamical criticality. In this work, the authors show that both nonequilibrium and quantum features can be simultaneously present and persist in the low-frequency properties of a critical one-dimensional driven open Bose gas, and no effective equilibrium description is applicable for this novel type of nonequilibrium quantum criticality.
Originally, the term ‘dynamic critical phenomena’ was coined for time-dependent properties near second-order phase transitions in thermal equilibrium . The kinetics of phase transitions in magnets, at the gas–liquid transition, and at the normal- to superfluid phase transition in helium 4 were among the prominent examples investigated already in the 1960s. The dynamic scaling hypothesis , generalizing the scaling ansatz for the static correlation function and introducing an additional dynamic critical exponent, successfully described a variety of these experiments. Yet only the development of the systematic renormalization group (RG) approach for critical phenomena in the subsequent decade provided a solid conceptual foundation for phenomenological scaling theories. Supplemented with exact solutions for certain idealized model systems, and guided by invaluable input from computer simulations in addition to experimental data, the renormalization group now provides a general framework to explore not only the static and dynamic properties near a critical point, but also the large-scale and low-frequency response in stable thermodynamic phases. Scaling concepts and the renormalization group have also been successfully applied to phase transitions at zero temperature driven by quantum rather than thermal fluctuations. It is to be hoped that RG methods may help to classify the strikingly rich phenomena encountered in far-from-equilibrium systems as well. Recent advances in studies of simple reaction-diffusion systems, active to absorbing state phase transitions, driven lattice gases, and scaling properties of moving interfaces and growing surfaces, among others, appear promising in this respect.
The Bose-Hubbard model provides a foundational paradigm for exploring quantum phase transitions in many-body systems. This thesis presents a systematic investigation into this model and its extensions, designed to provide a clear path for understanding both the rich underlying physics and the sophisticated numerical methods required for its study. Our approach is sequential: we begin with the standard one-dimensional Bose-Hubbard model, introduce complexity via the extended model with long-range interactions, and conclude by analyzing the impact of dissipation in a cavity-coupled open quantum system.To navigate these regimes, we implement and apply a suite of powerful computational techniques, including Density Matrix Renormalization Group (DMRG), finite-temperature Quantum Monte Carlo (QMC), and Mean-Field Theory (MFT). A significant component of this work is the detailed exposition of the implementation and logic of these numerical methods. Through their comparative application, we precisely characterize the equilibrium phase diagrams and benchmark the capabilities of each method. Crucially, our analysis of the open-system dynamics reveals that dissipation replaces the equilibrium phase diagram with one governed by non-equilibrium steady states (NESS), where the system evolves to either a stable solution or a persistent limit cycle.As such, this thesis is intended to serve a dual purpose: it is both a rigorous physical study of quantum phase transitions in a condensed matter system and a selfcontained pedagogical guide for researchers beginning to explore the phenomenology of quantum phase transitions through numerical schemes.