Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Quantum Lifshitz transitions generated by order from quantum disorder in strongly correlated Rashba spin-orbit-coupled systems

Fadi Sun, Jinwu Ye

Published Sep 29, 2021• 2 citations
Publisher

Abstract

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 $\text{U}(1)$ 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 $S$ limits. Experimental implications on cold atoms and some $4d$ or $5d$ Kitaev materials are discussed.

DOI
10.1103/physreva.104.l031306

Related papers

Quantum Lifshitz transitions generated by order from quantum disorder in strongly correlated Rashba spin-orbital coupled systems

Fadi Sun, Jinwu Ye

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.

arXiv:2202.12068•Feb 24, 2022•0 citations

In-commensurate Skyrmion crystals, devil staircases and multi-fractals due to spin orbit coupling in a lattice system

Fadi Sun, Jinwu Ye

In this advance, we study the system of strongly interacting spinor bosons in a square lattice subject to any of the linear combinations of the Rashba and Dresselhaus spin-orbit coupling (SOC). The SOC leads to novel and rich quantum and topological phenomena in a lattice system. They include masses generated from order from quantum disorder mechanism, collinear spin-bond correlated magnetic phase, quantum commensurate ( C ) and In-commensurate ( IC ) non-coplanar Skyrmion crystal phases, stripe co-planar ( spiral ) C and IC phases, quantum Lifshitz C-IC transitions, metastable states, hysteresis, topological rational and irrational winding numbers, incomplete and complete devil staircases, Cantor sets, multi-fractals, etc. Various perspectives and possible intimate connections with topological spin liquids due to geometric frustrations or quantum spin glass due to quenched disorders are discussed. Implications on current or near future cold atom systems and on 4d or 5d strongly correlated materials with SOC are discussed.

•Mar 1, 2016•1 citation

Quantum incommensurate skyrmion crystals and commensurate to in-commensurate transitions in cold atoms and materials with spin–orbit couplings in a Zeeman field

Fadi Sun, Jinwu Ye, Wu‐Ming Liu

In this work, we study strongly interacting spinor atoms in a lattice subject to a two dimensional (2d) anisotropic Rashba type of spin orbital coupling (SOC) and an Zeeman field. We find the interplay between the Zeeman field and the SOC provides a new platform to host rich and novel classes of quantum commensurate and in-commensurate phases, excitations and phase transitions. These commensurate phases include two collinear states at low and high Zeeman field, two co-planar canted states at mirror reflected SOC parameters respectively. Most importantly, there are non-coplanar incommensurate Skyrmion (IC-SkX) crystal phases surrounded by the four commensurate phases. New excitation spectra above all the five phases, especially on the IC-SKX phase are computed. Three different classes of quantum commensurate to in-commensurate transitions from the IC-SKX to its four neighboring commensurate phases are identified. Finite temperature behaviors and transitions are discussed. The critical temperatures of all the phases can be raised above that reachable by current cold atom cooling techniques simply by tuning the number of atoms N per site. In view of recent impressive experimental advances in generating 2d SOC for cold atoms in optical lattices, these new many-body phenomena can be explored in the current and near future cold atom experiments. Applications to various materials such as MnSi, Fe 0.5 Co 0.5 Si, especially the complex incommensurate magnetic ordering in Li 2 IrO 3 are given.

arXiv:1502.05338•New Journal of Physics•Aug 16, 2017•13 citations

Exotic spin phases in two-dimensional spin-orbit coupled models: Importance of quantum effects

Chao Wang, Ming Gong, Yong‐Jian Han +2 more

We investigate the phase diagrams of the effective spin models derived from Fermi-Hubbard and Bose-Hubbard models with Rashba spin-orbit coupling, using string bond states, one of the quantum tensor network states methods. We focus on the role of quantum fluctuation effect in stabilizing the exotic spin phases in these models. For boson systems, and when the ratio between interparticle and intraparticle interaction $\ensuremath{\lambda}>1$, the out-of-plane ferromagnetic (FM) and antiferromagnetic (AFM) phases obtained from quantum simulations are the same as those obtained from the classic model. However, the quantum order-by-disorder effect reduces the classical in-plane XY-FM and XY-vortex phases to the quantum X/Y-FM and X/Y-stripe phase when $\ensuremath{\lambda}<1$. The spiral phase and skyrmion phase can be realized in the presence of quantum fluctuation. For the Fermi-Hubbard model, the quantum fluctuation energies are always important in the whole parameter regime. A general picture to understand the phase diagrams from a symmetry point of view is also presented.

arXiv:1701.07722•Physical review. B./Physical review. B•Sep 12, 2017•6 citations

Fermionic Hubbard model with Rashba or Dresselhaus spin–orbit coupling

Fadi Sun, Jinwu Ye, Wu-Ming Liu

In this work, we investigate the possible dramatic effects of Rashba or Dresselhaus spin–orbit coupling (SOC) on the fermionic Hubbard model in a two-dimensional square lattice. In the strong coupling limit, it leads to the rotated antiferromagnetic Heisenberg model 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 subject to strong quantum fluctuations at T = 0. We evaluate the quantum fluctuations by the spin wave expansion up to order . In some SOC parameter regimes, the Y-y state supports a massive relativistic incommensurate magnon (C-IC) with its two gap minima positions continuously tuned by the SOC parameters. The C-IC magnons dominate all the low temperature thermodynamic quantities and also lead to the separation of the peak positions between the longitudinal and the transverse spin structure factors. In the weak coupling limit, any weak repulsive interaction also leads to a weak Y-y state. There is only a crossover from the weak to the strong coupling. High temperature expansions of the specific heats in both weak and strong coupling are presented. The dramatic roles to be played by these C-IC magnons at generic SOC parameters or under various external probes are hinted at. Experimental applications to both layered noncentrosymmetric materials and cold atoms are discussed.

arXiv:1601.01642•New Journal of Physics•Apr 20, 2017•14 citations

Frustrated superfluids in a non-Abelian flux

Fadi Sun, Junsen Wang, Jinwu Ye +1 more

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.

arXiv:1712.06545•Dec 18, 2017•0 citations
We study the system of strongly interacting spinor bosons in a square lattice subject to the isotropic Rashba spin-orbit coupling \ensuremathα=\ensuremathβ\ensuremath{\alpha}=\ensuremath{\beta}\ensuremathα=\ensuremathβ. 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×\else\texttimes\fi33\ifmmode\times\else\texttimes\fi{}33\ifmmode×\else\texttimes\fi3 Skyrmion crystal phase. The state at the Abelian point \ensuremathα=\ensuremathβ=\ensuremathπ/2\ensuremath{\alpha}=\ensuremath{\beta}=\ensuremath{\pi}/2\ensuremathα=\ensuremathβ=\ensuremathπ/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 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.
In this advance, we study the system of strongly interacting spinor bosons in a square lattice subject to any of the linear combinations of the Rashba and Dresselhaus spin-orbit coupling (SOC). The SOC leads to novel and rich quantum and topological phenomena in a lattice system. They include masses generated from order from quantum disorder mechanism, collinear spin-bond correlated magnetic phase, quantum commensurate ( C ) and In-commensurate ( IC ) non-coplanar Skyrmion crystal phases, stripe co-planar ( spiral ) C and IC phases, quantum Lifshitz C-IC transitions, metastable states, hysteresis, topological rational and irrational winding numbers, incomplete and complete devil staircases, Cantor sets, multi-fractals, etc. Various perspectives and possible intimate connections with topological spin liquids due to geometric frustrations or quantum spin glass due to quenched disorders are discussed. Implications on current or near future cold atom systems and on 4d or 5d strongly correlated materials with SOC are discussed.
In this work, we study strongly interacting spinor atoms in a lattice subject to a two dimensional (2d) anisotropic Rashba type of spin orbital coupling (SOC) and an Zeeman field. We find the interplay between the Zeeman field and the SOC provides a new platform to host rich and novel classes of quantum commensurate and in-commensurate phases, excitations and phase transitions. These commensurate phases include two collinear states at low and high Zeeman field, two co-planar canted states at mirror reflected SOC parameters respectively. Most importantly, there are non-coplanar incommensurate Skyrmion (IC-SkX) crystal phases surrounded by the four commensurate phases. New excitation spectra above all the five phases, especially on the IC-SKX phase are computed. Three different classes of quantum commensurate to in-commensurate transitions from the IC-SKX to its four neighboring commensurate phases are identified. Finite temperature behaviors and transitions are discussed. The critical temperatures of all the phases can be raised above that reachable by current cold atom cooling techniques simply by tuning the number of atoms N per site. In view of recent impressive experimental advances in generating 2d SOC for cold atoms in optical lattices, these new many-body phenomena can be explored in the current and near future cold atom experiments. Applications to various materials such as MnSi, Fe 0.5 Co 0.5 Si, especially the complex incommensurate magnetic ordering in Li 2 IrO 3 are given.
We investigate the phase diagrams of the effective spin models derived from Fermi-Hubbard and Bose-Hubbard models with Rashba spin-orbit coupling, using string bond states, one of the quantum tensor network states methods. We focus on the role of quantum fluctuation effect in stabilizing the exotic spin phases in these models. For boson systems, and when the ratio between interparticle and intraparticle interaction $\ensuremath{\lambda}>1$, the out-of-plane ferromagnetic (FM) and antiferromagnetic (AFM) phases obtained from quantum simulations are the same as those obtained from the classic model. However, the quantum order-by-disorder effect reduces the classical in-plane XY-FM and XY-vortex phases to the quantum X/Y-FM and X/Y-stripe phase when $\ensuremath{\lambda}<1$. The spiral phase and skyrmion phase can be realized in the presence of quantum fluctuation. For the Fermi-Hubbard model, the quantum fluctuation energies are always important in the whole parameter regime. A general picture to understand the phase diagrams from a symmetry point of view is also presented.
In this work, we investigate the possible dramatic effects of Rashba or Dresselhaus spin–orbit coupling (SOC) on the fermionic Hubbard model in a two-dimensional square lattice. In the strong coupling limit, it leads to the rotated antiferromagnetic Heisenberg model 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 subject to strong quantum fluctuations at T = 0. We evaluate the quantum fluctuations by the spin wave expansion up to order . In some SOC parameter regimes, the Y-y state supports a massive relativistic incommensurate magnon (C-IC) with its two gap minima positions continuously tuned by the SOC parameters. The C-IC magnons dominate all the low temperature thermodynamic quantities and also lead to the separation of the peak positions between the longitudinal and the transverse spin structure factors. In the weak coupling limit, any weak repulsive interaction also leads to a weak Y-y state. There is only a crossover from the weak to the strong coupling. High temperature expansions of the specific heats in both weak and strong coupling are presented. The dramatic roles to be played by these C-IC magnons at generic SOC parameters or under various external probes are hinted at. Experimental applications to both layered noncentrosymmetric materials and cold atoms are discussed.
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.