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CRC Press eBooks

Cluster Monte Carlo Algorithms for Dissipative Quantum Phase Transitions

Philipp Werner, Matthias Troyer

Published Nov 2, 2010• 0 citations
Publisher

Abstract

Dissipation and decoherence in quantum systems have important practical implications, from stabilizing superconductivity in granular materials, to the loss of information stored in qubits. In the models we consider in this chapter, energy dissipation is introduced by coupling a quantum mechanical degree of freedom to a bath of suitably chosen harmonic oscillators. The degrees of freedom of this bath can be integrated out analytically, which leads to an effective action with long-range interactions in imaginary time. We will review and present a number of recently developed efficient cluster Monte Carlo algorithms for various dissipative quantum systems. This chapter is based in large part on Refs. [1, 2] but has been updated with more recent developments, especially in the applications section.

DOI
10.1201/b10273-30

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Cluster Monte Carlo Algorithms for Dissipative Quantum Systems

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We review efficient Monte Carlo methods for simulating quantum systems which couple to a dissipative environment. A brief introduction of the Caldeira-Leggett model and the Monte Carlo method will be followed by a detailed discussion of cluster algorithms and the treatment of long-range interactions. Dissipative quantum spins and resistively shunted Josephson junctions will be considered. Dissipation and decoherence in quantum systems have important practical implications, from stabilizing superconductivity in granular materials, to the loss of information stored in qubits. In all the models we study, energy dissipation is introduced by coupling a quantum mechanical degree of freedom to a bath of suitably

•Jan 1, 2005•8 citations

Cluster Monte Carlo Algorithms for Dissipative Quantum Systems

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Dissipation, Quantum Phase Transitions, and Measurement

Sudip Chakravarty

Sudip Chakravarty Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, CA 90095-1547, U.S.A. This chapter reflects my subjective choice of topics. My interest falls into three distinct categories. The intense interest in the problem of dissipation in quantum systems began at the time when macroscopic quantum tunneling and coherence in superconducting quantum interference devices (SQUIDs) were proposed. This subject has seen considerable developments over the past three decades both in theory and in experiments [1]. An important problem in this subject is a particle in a double well potential coupled to a bath consisting of an infinite number of harmonic oscillators providing a linear dissipation to the particle, in other words coupled to an Ohmic heat bath in the language of electrical engineering [2]. Yet, it is hardly recognized that this problem constitutes one of the simplest models of quantum criticality [3]. Thus, unsurprisingly, little attention has been paid over the years to experimentally explore this critical phenomenon. It remains equally unrecognized that the same model holds a germ of the quantum-to-classical transition much discussed in measurement theory.1 Here I have attempted to draw a parallel with an even more elementary model of Coleman and Hepp [4], which actually contains no dissipation. Nonetheless the two problems are united by the dictum that for infinitely many degrees of freedom two distinct states of matter cannot be unitarily related. A particle in a double well coupled to a dissipative environment is indeed a system with an infinite number of degrees of freedom. Of course, the Coleman-Hepp model can be supplemented by dissipation to bring the two models closer, but the basic issue with respect to measurement is clearer in its original form.

CRC Press eBooks•Nov 2, 2010•0 citations

Interacting lattice systems with quantum dissipation: A quantum Monte Carlo study

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Focus on Quantum Dissipation in Unconventional Environments

Milena Grifoni, Elisabetta Paladino

Quantum dissipation has been the object of study within the physics and chemistry communities for many years. Despite this, the field is in constant evolution, largely due to the fact that novel systems where the understanding of dissipation and dephasing processes is of crucial importance have become experimentally accessible in recent years. Among the ongoing research themes, we mention the defeat of decoherence in solid state-based quantum bits (qubits) (e.g. superconducting qubits or quantum dot based qubits), or dissipation due to non-equilibrium Fermi reservoirs, as is the case for quantum transport through meso- and nanoscale structures. A close inspection of dissipation in such systems reveals that one has to deal with 'unconventional' environments, where common assumptions of, for example, linearity of the bath and/or equilibrium reservoir have to be abandoned. Even for linear baths at equilibrium it might occur that the bath presents some internal structure, due, for example, to the presence of localized bath modes. A large part of this focus issue is devoted to topics related to the rapidly developing fields of quantum computation and information with solid state nanodevices. In these implementations, single and two-qubit gates as well as quantum information transmission takes place in the presence of broadband noise that is typically non-Markovian and nonlinear. On both the experimental and theory side, understanding and defeating such noise sources has become a crucial step towards the implementation of efficient nanodevices. On a more fundamental level, electron and spin transport through quantum dot nanostructures may suffer from 'unconventional' dissipation mechanisms such as the simultaneous presence of spin relaxation and fermionic dissipation, or may represent themselves out of equilibrium baths for nearby mesoscopic systems. Finally, although not expected from the outset, the present collection of articles has revealed that different 'unconventional' questions were still open on the standard harmonic oscillator and spin baths. This includes both fundamental issues, such as the possibility of estimating the specific heat for a free particle in the presence of dissipation, and the development of methods suitable to dealing with long range correlations at zero temperature and with quantum chaotic environments. We believe that the present focus issue on Quantum Dissipation in Unconventional Environments , although certainly not exhaustive, provides an important open-access resource that presents the latest state of the art of research in this field along its different lines. Focus on Quantum Dissipation in Unconventional Environments Contents Coherent control of an effective two-level system in a non-Markovian biomolecular environment J Eckel, J H Reina and M Thorwart Charge transfer dynamics in driven molecular ratchets: quantum Monte Carlo results and rate models L Mühlbacher and J Ankerhold Decoherence in qubits due to low-frequency noise J Bergli, Y M Galperin and B L Altshuler Dephasing by electron–electron interactions in a ballistic Mach–Zehnder interferometer Clemens Neuenhahn and Florian Marquardt Quantum frustration of dissipation by a spin bath D D Bhaktavatsala Rao, Heiner Kohler and Fernando Sols A random matrix theory of decoherence T Gorin, C Pineda, H Kohler and T H Seligman Dissipative dynamics of a biased qubit coupled to a harmonic oscillator: analytical results beyond the rotating wave approximation Johannes Hausinger and Milena Grifoni Dissipative dynamics of a two-level system resonantly coupled to a harmonic mode Frederico Brito and Amir O Caldeira Spin correlations in spin blockade Rafael Sánchez, Sigmund Kohler and Gloria Platero Landau–Zener tunnelling in dissipative circuit QED David Zueco, Peter Hänggi and Sigmund Kohler Quantum oscillations in the spin-boson model: reduced visibility from non-Markovian effects and initial entanglement F K Wilhelm Dynamics of dissipative coupled spins: decoherence, relaxation and effects of a spin-boson bath P Nägele, G Campagnano and U Weiss Spin chain model for correlated quantum channels Davide Rossini, Vittorio Giovannetti and Simone Montangero Finite quantum dissipation: the challenge of obtaining specific heat Peter Hänggi, Gert-Ludwig Ingold and Peter Talkner Dynamics of large anisotropic spin in a sub-ohmic dissipative environment close to a quantum-phase transition Frithjof B Anders Effects of low-frequency noise cross-correlations in coupled superconducting qubits A D'Arrigo, A Mastellone, E Paladino and G Falci From coherent motion to localization: dynamics of the spin-boson model at zero temperature Haobin Wang and Michael Thoss Phonon distributions of a single-bath mode coupled to a quantum dot F Cavaliere, G Piovano, E Paladino and M Sassetti

New Journal of Physics•Nov 20, 2008•6 citations
Dissipation and decoherence in quantum systems have important practical implications, from stabilizing superconductivity in granular materials, to the loss of information stored in qubits. In the models we consider in this chapter, energy dissipation is introduced by coupling a quantum mechanical degree of freedom to a bath of suitably chosen harmonic oscillators. The degrees of freedom of this bath can be integrated out analytically, which leads to an effective action with long-range interactions in imaginary time. We will review and present a number of recently developed efficient cluster Monte Carlo algorithms for various dissipative quantum systems. This chapter is based in large part on Refs. [1, 2] but has been updated with more recent developments, especially in the applications section.
We review efficient Monte Carlo methods for simulating quantum systems which couple to a dissipative environment. A brief introduction of the Caldeira-Leggett model and the Monte Carlo method will be followed by a detailed discussion of cluster algorithms and the treatment of long-range interactions. Dissipative quantum spins and resistively shunted Josephson junctions will be considered. Dissipation and decoherence in quantum systems have important practical implications, from stabilizing superconductivity in granular materials, to the loss of information stored in qubits. In all the models we study, energy dissipation is introduced by coupling a quantum mechanical degree of freedom to a bath of suitably
Sudip Chakravarty Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, CA 90095-1547, U.S.A. This chapter reflects my subjective choice of topics. My interest falls into three distinct categories. The intense interest in the problem of dissipation in quantum systems began at the time when macroscopic quantum tunneling and coherence in superconducting quantum interference devices (SQUIDs) were proposed. This subject has seen considerable developments over the past three decades both in theory and in experiments [1]. An important problem in this subject is a particle in a double well potential coupled to a bath consisting of an infinite number of harmonic oscillators providing a linear dissipation to the particle, in other words coupled to an Ohmic heat bath in the language of electrical engineering [2]. Yet, it is hardly recognized that this problem constitutes one of the simplest models of quantum criticality [3]. Thus, unsurprisingly, little attention has been paid over the years to experimentally explore this critical phenomenon. It remains equally unrecognized that the same model holds a germ of the quantum-to-classical transition much discussed in measurement theory.1 Here I have attempted to draw a parallel with an even more elementary model of Coleman and Hepp [4], which actually contains no dissipation. Nonetheless the two problems are united by the dictum that for infinitely many degrees of freedom two distinct states of matter cannot be unitarily related. A particle in a double well coupled to a dissipative environment is indeed a system with an infinite number of degrees of freedom. Of course, the Coleman-Hepp model can be supplemented by dissipation to bring the two models closer, but the basic issue with respect to measurement is clearer in its original form.
Quantum dissipation arises when a large system can be split in a quantum system and an environment to which the energy of the former flows. Understanding the effect of dissipation on quantum many-body systems is of particular importance due to its potential relationship with quantum information. We propose a conceptually simple approach to introduce dissipation into interacting quantum systems in a thermodynamical context, in which every site of a one-dimensional (1D) lattice is coupled off-diagonally to its own bath. The interplay between quantum dissipation and interactions gives rise to counterintuitive interpretations such as a compressible zero-temperature state with spontaneous discrete symmetry breaking and a thermal phase transition in a 1D dissipative quantum many-body system as revealed by quantum Monte Carlo path-integral simulations.
Quantum dissipation has been the object of study within the physics and chemistry communities for many years. Despite this, the field is in constant evolution, largely due to the fact that novel systems where the understanding of dissipation and dephasing processes is of crucial importance have become experimentally accessible in recent years. Among the ongoing research themes, we mention the defeat of decoherence in solid state-based quantum bits (qubits) (e.g. superconducting qubits or quantum dot based qubits), or dissipation due to non-equilibrium Fermi reservoirs, as is the case for quantum transport through meso- and nanoscale structures. A close inspection of dissipation in such systems reveals that one has to deal with 'unconventional' environments, where common assumptions of, for example, linearity of the bath and/or equilibrium reservoir have to be abandoned. Even for linear baths at equilibrium it might occur that the bath presents some internal structure, due, for example, to the presence of localized bath modes. A large part of this focus issue is devoted to topics related to the rapidly developing fields of quantum computation and information with solid state nanodevices. In these implementations, single and two-qubit gates as well as quantum information transmission takes place in the presence of broadband noise that is typically non-Markovian and nonlinear. On both the experimental and theory side, understanding and defeating such noise sources has become a crucial step towards the implementation of efficient nanodevices. On a more fundamental level, electron and spin transport through quantum dot nanostructures may suffer from 'unconventional' dissipation mechanisms such as the simultaneous presence of spin relaxation and fermionic dissipation, or may represent themselves out of equilibrium baths for nearby mesoscopic systems. Finally, although not expected from the outset, the present collection of articles has revealed that different 'unconventional' questions were still open on the standard harmonic oscillator and spin baths. This includes both fundamental issues, such as the possibility of estimating the specific heat for a free particle in the presence of dissipation, and the development of methods suitable to dealing with long range correlations at zero temperature and with quantum chaotic environments. We believe that the present focus issue on Quantum Dissipation in Unconventional Environments , although certainly not exhaustive, provides an important open-access resource that presents the latest state of the art of research in this field along its different lines. Focus on Quantum Dissipation in Unconventional Environments Contents Coherent control of an effective two-level system in a non-Markovian biomolecular environment J Eckel, J H Reina and M Thorwart Charge transfer dynamics in driven molecular ratchets: quantum Monte Carlo results and rate models L Mühlbacher and J Ankerhold Decoherence in qubits due to low-frequency noise J Bergli, Y M Galperin and B L Altshuler Dephasing by electron–electron interactions in a ballistic Mach–Zehnder interferometer Clemens Neuenhahn and Florian Marquardt Quantum frustration of dissipation by a spin bath D D Bhaktavatsala Rao, Heiner Kohler and Fernando Sols A random matrix theory of decoherence T Gorin, C Pineda, H Kohler and T H Seligman Dissipative dynamics of a biased qubit coupled to a harmonic oscillator: analytical results beyond the rotating wave approximation Johannes Hausinger and Milena Grifoni Dissipative dynamics of a two-level system resonantly coupled to a harmonic mode Frederico Brito and Amir O Caldeira Spin correlations in spin blockade Rafael Sánchez, Sigmund Kohler and Gloria Platero Landau–Zener tunnelling in dissipative circuit QED David Zueco, Peter Hänggi and Sigmund Kohler Quantum oscillations in the spin-boson model: reduced visibility from non-Markovian effects and initial entanglement F K Wilhelm Dynamics of dissipative coupled spins: decoherence, relaxation and effects of a spin-boson bath P Nägele, G Campagnano and U Weiss Spin chain model for correlated quantum channels Davide Rossini, Vittorio Giovannetti and Simone Montangero Finite quantum dissipation: the challenge of obtaining specific heat Peter Hänggi, Gert-Ludwig Ingold and Peter Talkner Dynamics of large anisotropic spin in a sub-ohmic dissipative environment close to a quantum-phase transition Frithjof B Anders Effects of low-frequency noise cross-correlations in coupled superconducting qubits A D'Arrigo, A Mastellone, E Paladino and G Falci From coherent motion to localization: dynamics of the spin-boson model at zero temperature Haobin Wang and Michael Thoss Phonon distributions of a single-bath mode coupled to a quantum dot F Cavaliere, G Piovano, E Paladino and M Sassetti