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Bulletin of the American Physical Society

Precision auxiliary-field quantum Monte Carlo computations of Rashba spin-orbit coupling in interacting many-body systems

Peter Rosenberg, Hao Shi, Shiwei Zhang

Published Mar 7, 2018• 0 citations
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Strongly interacting many-body systems remain a central challenge of modern physics. Recent developments in the field of ultra-cold atomic physics have opened a new window onto this enduring problem. Experimental progress has revolutionized the approach to studying many-body systems and the exotic behaviors that emerge in these systems. It is now possible to engineer and directly measure a variety of models that can capture the essential features of real materials without the added complexity of disorder, impurities, or complicated or irregular geometries. The parameters of these models can be freely tuned with tremendous precision. These experimental realizations are an ideal setting in which to test and calibrate computational many-body methods that can provide insight and quantitative understanding to many of the open questions in condensed matter and many-body physics. in this thesis we study several models of strongly interacting many-fermion systems using cutting-edge numerical techniques including Hartree-Fock-Bogoliubov (HFB) mean-field theory and auxiliary-field quantum Monte Carlo (AFQMC). We explore the exotic phases and behaviors that emerge in these systems, beginning with finite-momentum pairing states in attractive spin-polarized fermions. We next demonstrate the unique capability of AFQMC to treat systems with spin-orbit coupling (SOC). We obtain high-precision, and in many cases numerically exact, results on SOC systems that can eventually be compared directly to experiment. The first system we highlight is the attractive Fermi gas with Rashba SOC, which displays unconventional pairing, charge, and spin properties. We then study the coexistence of charge and superfluid order, as well as topological signatures, in attractive lattice fermions with Rashba SOC. Our results provide a new, high-accuracy understanding of a strongly interacting many-body system and its exotic behaviors. These techniques can serve as a general framework for the treatment of strong interactions and SOC in many-body systems, and provide a foundation for future work on exotic phases in models and real materials.

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Strongly interacting many-body systems remain a central challenge of modern physics. Recent developments in the field of ultra-cold atomic physics have opened a new window onto this enduring problem. Experimental progress has revolutionized the approach to studying many-body systems and the exotic behaviors that emerge in these systems. It is now possible to engineer and directly measure a variety of models that can capture the essential features of real materials without the added complexity of disorder, impurities, or complicated or irregular geometries. The parameters of these models can be freely tuned with tremendous precision. These experimental realizations are an ideal setting in which to test and calibrate computational many-body methods that can provide insight and quantitative understanding to many of the open questions in condensed matter and many-body physics. in this thesis we study several models of strongly interacting many-fermion systems using cutting-edge numerical techniques including Hartree-Fock-Bogoliubov (HFB) mean-field theory and auxiliary-field quantum Monte Carlo (AFQMC). We explore the exotic phases and behaviors that emerge in these systems, beginning with finite-momentum pairing states in attractive spin-polarized fermions. We next demonstrate the unique capability of AFQMC to treat systems with spin-orbit coupling (SOC). We obtain high-precision, and in many cases numerically exact, results on SOC systems that can eventually be compared directly to experiment. The first system we highlight is the attractive Fermi gas with Rashba SOC, which displays unconventional pairing, charge, and spin properties. We then study the coexistence of charge and superfluid order, as well as topological signatures, in attractive lattice fermions with Rashba SOC. Our results provide a new, high-accuracy understanding of a strongly interacting many-body system and its exotic behaviors. These techniques can serve as a general framework for the treatment of strong interactions and SOC in many-body systems, and provide a foundation for future work on exotic phases in models and real materials.
The recent experimental realization of spin-orbit coupled Fermi gases provides a unique opportunity to study the interplay between strong interaction and spin-orbit coupling (SOC) in a tunable, disorder-free system. We present here precision ab initio numerical results on the two-dimensional, unpolarized, uniform Fermi gas with attractive interactions and Rashba SOC. Using the auxiliary-field quantum Monte Carlo method and incorporating recent algorithmic advances, we carry out exact calculations on sufficiently large system sizes to provide accurate results systematically as a function of experimental parameters. We obtain the equation of state, the momentum distributions, the pseudospin correlations, and the pair wave functions. Our results help illuminate the rich pairing structure induced by SOC, and provide benchmarks for theory and guidance to future experimental efforts.
Thanks to the recent experimental realization and control of artificial gauge fields, spin-orbit (SO) couplings are witnessing an ever increasing interest in the field of cold atoms. However, predicting their effect on spin polarization and energetic properties of interacting systems is a major challenge, due to the complex interplay between spin and position dynamics. In this work we exploit the diffusion Monte Carlo algorithm to compute energetic and polarization properties of a three-dimensional repulsive Fermi gas in the presence of Rashba spin-orbit coupling. We find that SO effects tend to contrast the spin alignment induced by the exchange interaction, slightly shifting the onset of the Stoner instability towards larger values of the scattering length. In addition, polarization and energy properties of the system can be tuned trough a combined control of the repulsive interaction and Rashba coupling.