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

arXiv:2202.09192 · Physical review. B./Physical review. B

Continuous phase transition from a chiral spin state to collinear magnetic order in a zigzag chain with Kitaev interactions

Rafael A. Macêdo, Flávia B. Ramos, Rodrigo G. Pereira

Published May 31, 2022• 3 citations
arXivHTMLPDF

Abstract

Quantum spin systems can break time-reversal symmetry by developing spontaneous magnetization or spin chirality. However, collinear magnets and chiral spin states are invariant under different symmetries, implying that the order parameter of one phase vanishes in the other. We show how to construct one-dimensional anisotropic spin models that exhibit a ``Landau-forbidden'' continuous phase transition between such states. As a concrete example, we focus on a zigzag chain with bond-dependent exchange and six-spin interactions. Using a combination of exact solutions, effective field theories, and numerical simulations, we show that the transition between the chiral and magnetic phases has an emergent $U(1)$ symmetry. The excitations governing the transition from the chiral phase can be pictured as mobile defects in a ${\mathbb{Z}}_{2}$ flux configuration which bind fermionic modes. We briefly discuss extensions to two dimensions and analogies with deconfined quantum criticality. Our results suggest new prospects for unconventional phase transitions involving chiral spin states.

DOI
10.1103/physrevb.105.205144

Related papers

Chiral spin state and nematic ferromagnet in the spin-1 Kitaev- Γ model

Qiang Luo, Jize Zhao, Jinbin Li +1 more

The higher-spin Kitaev magnets, in which the Kitaev interaction and off-diagonal exchange couplings are overwhelmingly large, have emerged as a fertile avenue to explore exotic phases and unusual excitations. In this paper, we study the quantum phase diagram of the spin-1 Kitaev-$\mathrm{\ensuremath{\Gamma}}$ model on the honeycomb lattice using density-matrix renormalization group. It harbors six distinct phases and the intriguing findings are three magnetically ordered phases in which both time-reversal symmetry and lattice symmetry, albeit of different sorts, are broken spontaneously. The chiral spin state originates from the order-by-disorder effect and exhibits an almost saturated scalar spin chirality at the quantum level. Depending on the relative strength of the two interactions, it also features a columnarlike or plaquettelike dimer pattern as a consequence of the translational symmetry breaking. In parallel, the nematic ferromagnets are situated at the ferromagnetic Kitaev side and possess small but finite ferromagnetic ordering. The lattice-rotational symmetry breaking enforces nonequivalent bond energy along one of the three bonds. Although the intrinsic difference between the two nematic ferromagnets remains elusive, the discontinuities in the von Neumann entropy, hexagonal plaquette operator, and Wilson loop operator convincingly suggest that they are separated via a first-order phase transition.

arXiv:2403.08382•Physical review. B./Physical review. B•Jul 8, 2024•8 citations

Chiral spin liquids at finite temperature in a three-dimensional Kitaev model

Yasuyuki Kato, Yoshitomo Kamiya, Joji Nasu +1 more

Chiral spin liquids (CSLs) in three dimensions and thermal phase transitions to paramagnet are studied by unbiased Monte Carlo simulations. For an extension of the Kitaev model to a three-dimensional tricoordinate network dubbed the hypernonagon lattice, we derive low-energy effective models in two different anisotropic limits. We show that the effective interactions between the emergent ${Z}_{2}$ degrees of freedom called fluxes are unfrustrated in one limit, while highly frustrated in the other. In both cases, we find a first-order phase transition to the CSL, where both time-reversal and parity symmetries are spontaneously broken. In the frustrated case, however, the CSL state is highly exotic---the flux configuration is subextensively degenerate while showing a directional order with broken ${C}_{3}$ rotational symmetry. Our results provide two contrasting archetypes of CSLs in three dimensions, both of which allow approximation-free simulation for investigating the thermodynamics.

arXiv:1707.02794•Physical review. B./Physical review. B•Nov 7, 2017•11 citations

Unconventional quantum phase transitions in a one-dimensional Lieb-Schultz-Mattis system

Wayne Zheng, D. N. Sheng, Yuan-Ming Lu

We study quantum phases and phase transitions in a one-dimensional interacting fermion system with a Lieb-Schultz-Mattis (LSM) type anomaly. Specifically, the inversion symmetry enforces any symmetry-preserving gapped ground state of the system to be a Kitaev chain, following an LSM type theorem that we prove. Alternatively, via the Jordan-Wigner transformation, this system describes a spin system whose gapped ground states must break either the inversion or the Ising symmetry associated with fermion parity. We obtain a phase diagram using analytical methods and variational matrix product state simulations and study the critical behaviors of the quantum phase transitions therein using entanglement entropy, energy variance, and finite-size scaling of order parameters. In particular, we observe a continuous phase transition between two ordered phases that are beyond the Ginzburg-Landau-Wilson paradigm, in analogy to the deconfined quantum critical points in two spatial dimensions. We show this type of a 1D deconfined quantum critical point is described by the Tomonaga-Luttinger liquid theory and extract its Luttinger parameter and critical exponents. We also identify a gapless phase that emerges from a deconfined quantum critical point between two ordered phases, which cannot be described by a U(1) Luttinger liquid.

arXiv:2109.04019•Physical review. B./Physical review. B•Feb 25, 2022•9 citations

Four-spin-exchange- and magnetic-field-induced chiral order in two-leg spin ladders

Masahiro Sato

We propose a mechanism of a vector chiral long-range order in two-leg spin-$\frac{1}{2}$ and spin-1 antiferromagnetic ladders with four-spin exchanges and a Zeeman term. It is known that for one-dimensional quantum systems, spontaneous breakdown of continuous symmetries is generally forbidden. Any vector chiral order hence does not appear in spin-rotationally [SU(2)]-symmetric spin ladders. However, if a magnetic field is added along the ${S}^{z}$ axis of ladders and the SU(2) symmetry is reduced to the U(1) one, the $z$ component of a vector chiral order can emerge with the remaining U(1) symmetry unbroken. Making use of Abelian bosonization techniques, we actually show that a certain type of four-spin exchange can yield a vector chiral long-range order in spin-$\frac{1}{2}$ and spin-1 ladders under a magnetic field. In the chiral-ordered phase, the ${Z}_{2}$ interchain-parity (i.e., chain-exchange) symmetry is spontaneously broken. We also consider effects of perturbations breaking the parity symmetry.

arXiv:cond-mat/0703396•Physical Review B•Aug 14, 2007•15 citations

Non-Landau quantum phase transition in modulated SU( N ) Heisenberg spin chains

Sylvain Capponi, Lukas Devos, P. Lecheminant +2 more

We investigate the nature of the quantum phase transition in modulated $\mathrm{SU}(N)$ Heisenberg spin chains. In the odd-$N$ case, the transition separates a trivial nondegenerate phase to a doubly degenerate gapped chiral $\mathrm{PSU}(N)$ symmetry-protected topological (SPT) phase which breaks spontaneously the inversion symmetry. The transition is not an Ising transition associated to the breaking of the ${\mathbb{Z}}_{2}$ inversion symmetry, but is governed by the delocalization of the edge states of the SPT phase. In this respect, a modulated $\mathrm{SU}(N)$ Heisenberg spin chain provides a simple example in one dimension of a non-Landau phase transition which is described by the $\mathrm{SU}{(N)}_{1}$ conformal field theory. We show that the chiral SPT phase exhibits fractionalized spinon excitations, which can be confined by slightly changing the model parameters.

arXiv:2409.01019•Physical review. B./Physical review. B•Jan 10, 2025•2 citations

Continuous transition between Ising magnetic order and a chiral spin liquid

G. Shankar, Chien-Hung Lin, Joseph Maciejko

The competition between fractionalized spin-liquid states and magnetically ordered phases is an important paradigm in frustrated magnetism. Spin-orbit coupled Mott insulators with Ising-like magnetic anisotropies, such as Kitaev materials, are a particularly rich playground to explore this competition. In this work, we use effective field theory methods to show that a direct quantum phase transition can occur in two-dimensional (2D) Ising spin systems between a topologically ordered chiral spin liquid and a phase with magnetic long-range order. Such a transition can be protected by lattice symmetries and is described by a theory of massless Majorana fields coupled to non-Abelian $\text{SO}(N)$ gauge fields with a Chern-Simons term. We further show that Euclidean Majorana zero modes bound to ${\mathbb{Z}}_{2}$ monopole-instantons in the emergent non-Abelian gauge field are key to understanding spontaneous symmetry breaking in the ordered phase.

arXiv:2207.02701•Physical review. B./Physical review. B•Dec 6, 2022•5 citations
Quantum spin systems can break time-reversal symmetry by developing spontaneous magnetization or spin chirality. However, collinear magnets and chiral spin states are invariant under different symmetries, implying that the order parameter of one phase vanishes in the other. We show how to construct one-dimensional anisotropic spin models that exhibit a ``Landau-forbidden'' continuous phase transition between such states. As a concrete example, we focus on a zigzag chain with bond-dependent exchange and six-spin interactions. Using a combination of exact solutions, effective field theories, and numerical simulations, we show that the transition between the chiral and magnetic phases has an emergent U(1)U(1)U(1) symmetry. The excitations governing the transition from the chiral phase can be pictured as mobile defects in a Z2{\mathbb{Z}}_{2}Z2​ flux configuration which bind fermionic modes. We briefly discuss extensions to two dimensions and analogies with deconfined quantum criticality. Our results suggest new prospects for unconventional phase transitions involving chiral spin states.
The higher-spin Kitaev magnets, in which the Kitaev interaction and off-diagonal exchange couplings are overwhelmingly large, have emerged as a fertile avenue to explore exotic phases and unusual excitations. In this paper, we study the quantum phase diagram of the spin-1 Kitaev-$\mathrm{\ensuremath{\Gamma}}$ model on the honeycomb lattice using density-matrix renormalization group. It harbors six distinct phases and the intriguing findings are three magnetically ordered phases in which both time-reversal symmetry and lattice symmetry, albeit of different sorts, are broken spontaneously. The chiral spin state originates from the order-by-disorder effect and exhibits an almost saturated scalar spin chirality at the quantum level. Depending on the relative strength of the two interactions, it also features a columnarlike or plaquettelike dimer pattern as a consequence of the translational symmetry breaking. In parallel, the nematic ferromagnets are situated at the ferromagnetic Kitaev side and possess small but finite ferromagnetic ordering. The lattice-rotational symmetry breaking enforces nonequivalent bond energy along one of the three bonds. Although the intrinsic difference between the two nematic ferromagnets remains elusive, the discontinuities in the von Neumann entropy, hexagonal plaquette operator, and Wilson loop operator convincingly suggest that they are separated via a first-order phase transition.
Chiral spin liquids (CSLs) in three dimensions and thermal phase transitions to paramagnet are studied by unbiased Monte Carlo simulations. For an extension of the Kitaev model to a three-dimensional tricoordinate network dubbed the hypernonagon lattice, we derive low-energy effective models in two different anisotropic limits. We show that the effective interactions between the emergent Z2{Z}_{2}Z2​ degrees of freedom called fluxes are unfrustrated in one limit, while highly frustrated in the other. In both cases, we find a first-order phase transition to the CSL, where both time-reversal and parity symmetries are spontaneously broken. In the frustrated case, however, the CSL state is highly exotic---the flux configuration is subextensively degenerate while showing a directional order with broken C3{C}_{3}C3​ rotational symmetry. Our results provide two contrasting archetypes of CSLs in three dimensions, both of which allow approximation-free simulation for investigating the thermodynamics.
We study quantum phases and phase transitions in a one-dimensional interacting fermion system with a Lieb-Schultz-Mattis (LSM) type anomaly. Specifically, the inversion symmetry enforces any symmetry-preserving gapped ground state of the system to be a Kitaev chain, following an LSM type theorem that we prove. Alternatively, via the Jordan-Wigner transformation, this system describes a spin system whose gapped ground states must break either the inversion or the Ising symmetry associated with fermion parity. We obtain a phase diagram using analytical methods and variational matrix product state simulations and study the critical behaviors of the quantum phase transitions therein using entanglement entropy, energy variance, and finite-size scaling of order parameters. In particular, we observe a continuous phase transition between two ordered phases that are beyond the Ginzburg-Landau-Wilson paradigm, in analogy to the deconfined quantum critical points in two spatial dimensions. We show this type of a 1D deconfined quantum critical point is described by the Tomonaga-Luttinger liquid theory and extract its Luttinger parameter and critical exponents. We also identify a gapless phase that emerges from a deconfined quantum critical point between two ordered phases, which cannot be described by a U(1) Luttinger liquid.
We propose a mechanism of a vector chiral long-range order in two-leg spin-12\frac{1}{2}21​ and spin-1 antiferromagnetic ladders with four-spin exchanges and a Zeeman term. It is known that for one-dimensional quantum systems, spontaneous breakdown of continuous symmetries is generally forbidden. Any vector chiral order hence does not appear in spin-rotationally [SU(2)]-symmetric spin ladders. However, if a magnetic field is added along the Sz{S}^{z}Sz axis of ladders and the SU(2) symmetry is reduced to the U(1) one, the zzz component of a vector chiral order can emerge with the remaining U(1) symmetry unbroken. Making use of Abelian bosonization techniques, we actually show that a certain type of four-spin exchange can yield a vector chiral long-range order in spin-12\frac{1}{2}21​ and spin-1 ladders under a magnetic field. In the chiral-ordered phase, the Z2{Z}_{2}Z2​ interchain-parity (i.e., chain-exchange) symmetry is spontaneously broken. We also consider effects of perturbations breaking the parity symmetry.
We investigate the nature of the quantum phase transition in modulated SU(N)\mathrm{SU}(N)SU(N) Heisenberg spin chains. In the odd-NNN case, the transition separates a trivial nondegenerate phase to a doubly degenerate gapped chiral PSU(N)\mathrm{PSU}(N)PSU(N) symmetry-protected topological (SPT) phase which breaks spontaneously the inversion symmetry. The transition is not an Ising transition associated to the breaking of the Z2{\mathbb{Z}}_{2}Z2​ inversion symmetry, but is governed by the delocalization of the edge states of the SPT phase. In this respect, a modulated SU(N)\mathrm{SU}(N)SU(N) Heisenberg spin chain provides a simple example in one dimension of a non-Landau phase transition which is described by the SU(N)1\mathrm{SU}{(N)}_{1}SU(N)1​ conformal field theory. We show that the chiral SPT phase exhibits fractionalized spinon excitations, which can be confined by slightly changing the model parameters.
The competition between fractionalized spin-liquid states and magnetically ordered phases is an important paradigm in frustrated magnetism. Spin-orbit coupled Mott insulators with Ising-like magnetic anisotropies, such as Kitaev materials, are a particularly rich playground to explore this competition. In this work, we use effective field theory methods to show that a direct quantum phase transition can occur in two-dimensional (2D) Ising spin systems between a topologically ordered chiral spin liquid and a phase with magnetic long-range order. Such a transition can be protected by lattice symmetries and is described by a theory of massless Majorana fields coupled to non-Abelian SO(N)\text{SO}(N)SO(N) gauge fields with a Chern-Simons term. We further show that Euclidean Majorana zero modes bound to Z2{\mathbb{Z}}_{2}Z2​ monopole-instantons in the emergent non-Abelian gauge field are key to understanding spontaneous symmetry breaking in the ordered phase.