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# Hubbard model with Rashba or Dresselhaus spin-orbit coupling and Rotated Anti-ferromagnetic Heisenberg Model

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### Abstract

In this work, we investigate Hubbard model subject to Rashba or Dresselhaus spin-orbit coupling (SOC). In the strong coupling limit, it leads to the Rotated Anti-ferromagnetic Heisenberg model (RAFHM) which is a new class of quantum spin model. For a special equivalent class, we identify a new spin-orbital entangled commensurate ground (Y-y) state suffering quantum fluctuations at $$T=0$$. We evaluate the quantum fluctuations by the spin wave expansion (SWE) up to order $$1/S^2$$. It supports a massive relativistic commensurate magnon C-C$$_0$$ in one SOC parameter regime and a new massive relativistic elementary excitation: in-commensurate magnon C-IC in the other regime. The C-IC encodes short-range incommensurate orders embedded in a commensurate phase with its gap minimum positions (in momentum space) continuously tuned by the SOC strength. At both $$T=0$$ and low temperatures, these relativistic magnons lead to dramatic effects in many physical quantities such as specific heat, magnetization, $$(0,\pi)$$ and $$(\pi,0)$$ susceptibilities, Wilson ratio and spin correlation functions. In the weak coupling limit, any weak repulsive interaction also leads to the Y-y state. The crossover from the weak to the strong coupling is studied. High temperature expansions of the specific heats in both weak and strong coupling are presented. Experimental applications to both condense matter and cold atom systems are discussed.

### Most cited references13

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### In situ observation of incompressible Mott-insulating domains in ultracold atomic gases.

(2009)
The observation of the superfluid to Mott insulator phase transition of ultracold atoms in optical lattices was an enabling discovery in experimental many-body physics, providing the first tangible example of a quantum phase transition (one that occurs even at zero temperature) in an ultracold atomic gas. For a trapped gas, the spatially varying local chemical potential gives rise to multiple quantum phases within a single sample, complicating the interpretation of bulk measurements. Here we report spatially resolved, in-situ imaging of a two-dimensional ultracold atomic gas as it crosses the superfluid to Mott insulator transition, providing direct access to individual characteristics of the insulating, superfluid and normal phases. We present results for the local compressibility in all phases, observing a strong suppression in the insulator domain and suppressed density fluctuations for the Mott insulator, in accordance with the fluctuation-dissipation theorem. Furthermore, we obtain a direct measure of the finite temperature of the system. Taken together, these methods enable a complete characterization of multiple phases in a strongly correlated Bose gas, and of the interplay between quantum and thermal fluctuations in the quantum critical regime.
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### Revealing the Superfluid Lambda Transition in the Universal Thermodynamics of a Unitary Fermi Gas

(2011)
We have observed the superfluid phase transition in a strongly interacting Fermi gas via high-precision measurements of the local compressibility, density and pressure down to near-zero entropy. Our data completely determine the universal thermodynamics of strongly interacting fermions without any fit or external thermometer. The onset of superfluidity is observed in the compressibility, the chemical potential, the entropy, and the heat capacity. In particular, the heat capacity displays a characteristic lambda-like feature at the critical temperature of $$T_c/T_F = 0.167(13)$$. This is the first clear thermodynamic signature of the superfluid transition in a spin-balanced atomic Fermi gas. Our measurements provide a benchmark for many-body theories on strongly interacting fermions, relevant for problems ranging from high-temperature superconductivity to the equation of state of neutron stars.
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### Using photoemission spectroscopy to probe a strongly interacting Fermi gas

(2008)
Ultracold atom gases provide model systems in which many-body quantum physics phenomena can be studied. Recent experiments on Fermi gases have realized a phase transition to a Fermi superfluid state with strong interparticle interactions. This system is a realization of the BCS-BEC crossover connecting the physics of BCS superconductivity and that of Bose-Einstein condensation (BEC). While many aspects of this system have been investigated, it has not yet been possible to measure the single-particle excitation spectrum, which is a fundamental property directly predicted by many-body theories. Here we show that the single-particle spectral function of the strongly interacting Fermi gas at T ~ Tc is dramatically altered in a way that is consistent with a large pairing gap. We use photoemission spectroscopy to directly probe the elementary excitations and energy dispersion in the Fermi gas of atoms. In these photoemission experiments, an rf photon ejects an atom from our strongly interacting system via a spin-flip transition to a weakly interacting state. We measure the occupied single-particle density of states for an ultracold Fermi gas of 40-potassium atoms at the cusp of the BCS-BEC crossover and on the BEC side of the crossover, and compare these results to that for a nearly ideal Fermi gas. Our results probe the many-body physics in a way that could be compared to data for high-Tc superconductors. This new measurement technique for ultracold atom gases, like photoemission spectroscopy for electronic materials, directly probes low energy excitations and thus can reveal excitation gaps and/or pseudogaps. Furthermore, this technique can provide an analog to angle-resolved photoemission spectroscopy (ARPES) for probing anisotropic systems, such as atoms in optical lattice potentials.
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### Author and article information

###### Journal
1601.01642

Condensed matter, Quantum gases & Cold atoms