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arXiv:1712.06545

Frustrated superfluids in a non-Abelian flux

Fadi Sun, Junsen Wang, Jinwu Ye, Youjin Deng

Published Dec 18, 2017• 0 citations
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Abstract

We study possible superfluid states of the Rashba spin-orbit coupled (SOC) spinor bosons with the spin anisotropic interaction $ λ$ hopping in a square lattice. The frustrations from the non-abelian flux due to the SOC leads to novel spin-bond correlated superfluids. By using a recently developed systematic "order from quantum disorder" analysis, we not only determine the true quantum ground state, but also evaluate the mass gap in the spin sector at $ λ< 1 $, especially compute the the excitation spectrum of the Goldstone mode in the spin sector at $ λ=1 $ which would be quadratic without the analysis. The analysis also leads to different critical exponents on the two sides of the 2nd order transition driven by a roton touchdown at $ λ=1 $. The intimate analogy at $ λ=1 $ with the charge neutral Goldstone mode in the pseudo-spin sector in the Bilayer quantum Hall systems at the total filling factor $ ν_T=1 $ are stressed. The experimental implications and detections of these novel phenomena in cold atoms loaded on a optical lattice are presented.

DOI
10.48550/arxiv.1712.06545

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We study possible superfluid states of the Rashba spin-orbit coupled (SOC) spinor bosons with the spin anisotropic interaction λ λλ hopping in a square lattice. The frustrations from the non-abelian flux due to the SOC leads to novel spin-bond correlated superfluids. By using a recently developed systematic "order from quantum disorder" analysis, we not only determine the true quantum ground state, but also evaluate the mass gap in the spin sector at λ<1λ< 1λ<1, especially compute the the excitation spectrum of the Goldstone mode in the spin sector at λ=1λ=1λ=1 which would be quadratic without the analysis. The analysis also leads to different critical exponents on the two sides of the 2nd order transition driven by a roton touchdown at λ=1λ=1λ=1. The intimate analogy at λ=1λ=1λ=1 with the charge neutral Goldstone mode in the pseudo-spin sector in the Bilayer quantum Hall systems at the total filling factor νT=1ν_T=1νT​=1 are stressed. The experimental implications and detections of these novel phenomena in cold atoms loaded on a optical lattice are presented.
Inspired by recent experimental advances to generate Abelian flux for neutral cold atoms and photons moving in a lattice, we investigate the possible effects of the $ \pi $ flux through a unit cell in the pseudo-spin 1/2 spinor boson Hubbard model in a square lattice. We find that the $ \pi $ flux induces a dramatic interplay between the charge and the spin which leads to a frustrated superfluid. We develop a new and systematic order from quantum disorder analysis to determine not only the true quantum ground state, but also the excitation spectrum. The superfluid ground state has a 4 sublattice $ 90^{\circ} $ coplanar spin structure which supports 4 linear gapless modes with 3 different velocities. We speculate the transition from the weak coupling frustrated SF to the strong coupling Ferromagnetic Mott state to be in a new universality class of non-Ginsburg Landau type. These novel phenomena may be observed in these recent cold atom and photonic experiments.
We study possible many body phenomena in the Quantum Anomalous Hall system of weakly interacting spinor bosons in a square lattice. There are various novel spin-bond correlated superfluids (SF) and quantum or topological phase transitions among these SF phases. One transition is a first order one driven by roton droppings ( but with non-zero gaps $ Δ_R $ ) tuned by the Zeeman field $ h $. Another is a second order bosonic Lifshitz transition with the dynamic exponents $ z_x=z_y=2 $ and an accompanying $ [C_4 \times C_4]_D $ symmetry breaking. It is driven by the softening of the superfluid Goldstone mode tuned by the ratio of spin-orbit coupled (SOC) strength over the hopping strength. The two phase boundaries meet at a topological tri-critical (TT) point which separates the $ h=0 $ line into two SF phases with $ N=2 $ and $ N=4 $ condensation momenta respectively. At the $ h=0 $ line where the system has an anti-unitary $ Z_2 $ Reflection symmetry, there are infinite number of classically degenerate family of states on both sides. We perform a systematic order from quantum disorder analysis to find the quantum ground states, also calculate the roton gaps $ Δ_R $ generated by the order from disorder mechanism on both sides of the TT point. The $ N=2 $ and $ N=4 $ SF phases have the same spin-orbital XY-AFM spin structure, respect the anti-unitary symmetry and break the $ [C_4 \times C_4]_D $ symmetry, so they be distinguished only by the different topology of the BEC condensation momenta instead of by any differences in the symmetry breaking patterns. All these novel quantum or topological phenomena can be probed in the recent experimentally realized weakly interacting Quantum Anomalous Hall (QAH) model of $ ^87 Rb $ by Wu, {\sl et.al}, Science 354, 83-88 (2016).
We study the system of strongly interacting spinor bosons in a square lattice subject to the isotropic Rashba SOC $ α=β$. It supports collinear spin-bond correlated magnetic Y-x phase, a gapped in-commensurate (IC-) co-planar IC-XY-y phase, a non-coplanar commensurate (C-) $ 3 \times 3 $ Skyrmion crystal phase (SkX). The state at the Abelian point $ α=β=π/2 $ is just an AFM state in a rotated basis. Slightly away from the point, we identify a spurious $ U(1) $ symmetry, develop a novel and non-perturbative method to calculate not only the gap, but also the excitation spectrum due to the order from quantum disorder (OFQD) mechanism. We construct a symmetry based effective action to investigate the quantum Lifshitz transition from the Y-x state to the IC-XY-y state and establish the connection between the phenomenological parameters in the effective action and those evaluated by the microscopic non-perturbative OFQD analysis in the large $ S $ limits. Experimental implications on cold atoms and some 4d or 5d Kitaev materials are discussed.
We study the system of strongly interacting spinor bosons in a square lattice subject to the isotropic Rashba spin-orbit coupling $\ensuremath{\alpha}=\ensuremath{\beta}$. It supports a collinear spin-bond correlated magnetic Y-x phase, a gapped coplanar in-commensurate (IC) XY-y phase, and a noncoplanar commensurate (C) $3\ifmmode\times\else\texttimes\fi{}3$ Skyrmion crystal phase. The state at the Abelian point $\ensuremath{\alpha}=\ensuremath{\beta}=\ensuremath{\pi}/2$ is just a ferromagnetic state in a rotated basis. Slightly away from the point, we identify a spurious U(1)\text{U}(1)U(1) symmetry, develop a nonperturbative method to calculate not only the gap but also the excitation spectrum due to the order from quantum disorder (OFQD) mechanism. We construct a symmetry-based effective action to investigate the quantum Lifshitz transition from the Y-x state to the IC XY-y state and establish the connection between the phenomenological parameters in the effective action and those evaluated by the microscopic nonperturbative OFQD analysis in the large SSS limits. Experimental implications on cold atoms and some 4d4d4d or 5d5d5d Kitaev materials are discussed.
We study the system of attractively interacting fermions hopping in a square lattice with any linear combinations of Rashba or Dresselhaus spin-orbit coupling in a normal Zeeman field. By imposing self-consistence equations at half filling with zero chemical potential, we find that there are three phases: band insulator (BI), superfluid (SF), and topological superfluid (TSF) with a Chern number C=2C=2C=2. The C=2C=2C=2 TSF happens in small Zeeman fields and weak interactions which is in the experimentally most easily accessible regime. The transition from the BI to the SF is a first-order one due to the multiminima structure of the ground state energy landscape. There is a class of topological phase transitions (TPTs) from the SF to the C=2C=2C=2 TSF at the low critical field hc1{h}_{c1}hc1​, then another one from the C=2C=2C=2 TSF to the BI at the upper critical field hc2{h}_{c2}hc2​. We derive effective actions to describe these two classes of topological phase transitions, then use them to study the Majorana edge modes and the zero modes inside the vortex core of the C=2C=2C=2 TSF near both hc1{h}_{c1}hc1​ and hc2{h}_{c2}hc2​, especially exploring their spatial and spin structures. We find that the edge modes decay into the bulk with oscillating behaviors and determine both the decay and oscillating lengths. We compute the bulk spectra and map out the Berry curvature distribution in momentum space near both hc1{h}_{c1}hc1​ and hc2{h}_{c2}hc2​. We elaborate some intriguing bulk-Berry curvature-edge-vortex correspondences. We also discuss the competitions between SFs and charge density wave states in more general cases. A possible classification scheme of all the TPTs in a square lattice is outlined. Comparisons with previous works on related systems are discussed. Possible experimental implications in cold atoms in an optical lattice are given.
Abstract The order from quantum disorders (OFQD) phenomenon is well-known and ubiquitous in particle physics and frustrated magnetic systems. Typically, OFQD transfers a spurious Goldstone mode into a pseudo-Goldstone mode with a tiny gap. Here, we report an opposite phenomenon: OFQD transfers a spurious quadratic mode into a true linear Goldstone mode with a very small velocity (named slow-Goldstone mode). This new phenomenon is demonstrated in an interacting bosonic system subjected to an Abelian flux. We develop a new and systematic OFQD analysis to determine the true quantum ground state and the whole excitation spectrum. In the weak-coupling limit, the superfluid ground state has a 4-sublattice 90° coplanar spin structure, which supports 4 linear Goldstone modes with 3 different velocities. One of which is generated by the OFQD is much softer than the other 3 Goldstone modes, so it can be easily detected in the cold atom or photonic experiments. In the strong-coupling limit, the ferromagnetic Mott ground state with a true quadratic Goldstone mode. We speculate that there could be some topological phases intervening between the two symmetry broken states. These novel phenomena may be observed in the current cold-atom or photonic experiments subjected to an Abelian flux at the weak coupling limit where the heatings may be well under control. Possible connections to Coleman-Weinberg potential in particle physics, 1/N expansion of Sachdev-Ye-Kitaev models and zero temperature quantum black hole entropy are outlined.