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:1606.04927 · Physical review. B./Physical review. B

Quantum phase transitions in a generalized compass chain with three-site interactions

Wen‐Long You, Yu-Cheng Qiu, Andrzej M. Oleś

Published Jun 15, 2016• 29 citations
arXivHTMLPDF

Abstract

We consider a class of one-dimensional compass models with an XYZ-YZX type of three-site exchange interaction in an external magnetic field. We present the exact solution derived by means of Jordan-Wigner transformation, and study the excitation gap, spin correlations, and establish the phase diagram. Besides the canted antiferromagnetic and polarized phases, the three-site interactions induce two distinct chiral phases, corresponding to gapless spinless-fermion systems having two or four Fermi points. We find that the $z$ component of the scalar chirality operator can act as an order parameter for these chiral phases. We also find that the thermodynamic quantities including the Wilson ratio can characterize the liquid phases. Finally, a nontrivial magnetoelectric effect is explored, and we show that the polarization can be manipulated by the magnetic field in the absence of electric field.

DOI
10.1103/physrevb.93.214417

Related papers

Exact treatment of magnetism-driven ferroelectricity in the one-dimensional compass model

Wen‐Long You, Guanghua Liu, Peter Horsch +1 more

We consider a class of one-dimensional compass models with antisymmetric Dzyaloshinskii-Moriya exchange interaction in an external magnetic field. Based on the exact solution derived by means of Jordan-Wigner transformation, we study the excitation gap, spin correlations, ground-state degeneracy, and critical properties at phase transitions. The phase diagram at finite electric and magnetic field consists of three phases: ferromagnetic, canted antiferromagnetic, and chiral. Dzyaloshinskii-Moriya interaction induces an electrical polarization in the ground state of the chiral phase, where the nonlocal string order and special features of entanglement spectra arise, while strong chiral correlations emerge at finite temperature in the other phases and are controlled by a gap between the nonchiral ground state and the chiral excitations. We further show that the magnetoelectric effects in all phases disappear above a typical temperature corresponding to the total bandwidth of the effective fermionic model. To this end we explore the entropy, specific heat, magnetization, electric polarization, and the magnetoelectric tensor at finite temperature. We identify rather peculiar specific-heat and polarization behavior of the compass model which follows from highly frustrated interactions.

arXiv:1409.5850•Physical Review B•Sep 19, 2014•30 citations

Quantum phase transitions of a generalized compass chain with staggered Dzyaloshinskii–Moriya interaction

Qing-Qiu Wu, Weihai Ni, Wen‐Long You

We consider a class of one-dimensional compass models with staggered Dzyaloshinskii-Moriya exchange interactions in an external transverse magnetic field. Based on the exact solution derived from Jordan-Wigner approach, we study the excitation gap, energy spectra, spin correlations and critical properties at phase transitions. We explore mutual effects of the staggered Dzyaloshinskii-Moriya interaction and the magnetic field on the energy spectra and the ground-state phase diagram. Thermodynamic quantities including the entropy and the specific heat are discussed, and their universal scalings at low temperature are demonstrated.

arXiv:1705.10937•Journal of Physics Condensed Matter•May 5, 2017•4 citations

Critical Phases of the extended isotropic $XY$ chain with four-spin interaction

Nika Kurdadze, G Gogaberishvili, G. Y. Japaridze

Using the Jordan-Wigner transformation we calculate exactly the ground state and low-temperature thermodynamic properties of the spin $S=1/2$ isotropic $XX$ chain with four spin interaction. In terms of the equivalent spinless fermion (SF) representation the system is viewed as a lattice fermion gas with nearest-neighbor ($J$) and next-next-next-neighbor ($J^{\ast}/4$) hopping. It is shown that with the increase of four spin coupling, at $J^{\ast}_{c} = 4J/3$ the system experiences the Lifshitz type topological phase transition characterized by the tripling of Fermi points. The quantum phase transition (QPT) point marks transition from a gapless spin-liquid phase of standard $XX$ chain into again a gapless spin-liquid phase with different character of power-low decay of spin correlations. At the transition point the free fermion dispersion relation shows flattering at Fermi points, what determines singular character of density of states $ρ(ω)\sim (ω/J)^{-2/3}$ and as a consequence unconventional temperature dependence of heat capacity of the system $C\sim (T/J^{\ast})^{1/3}$, and singular magnetic susceptibility of the system $χ(H)\sim (H/J^{\ast})^{-2/3}$. In the case of alternating magnetic field the system is characterized by the rich ground state phase diagram which contains fully polarized (ferromagnetic), gapped antiferromagnetic (AFM) and spin liquid phases. At the transition point from the gapped AFM phase into the gapless polarized spin liquid phase the system shows rapid increase of magnetization $m\sim(H-H_c)^{1/6}$ and magnetic susceptibility a singular behavior as $χ(H)\sim (H-H_c)^{-5/6}$.

arXiv:2607.29006•Jul 31, 2026•0 citations

Quantum phase transitions in exactly solvable one-dimensional compass models

Wen‐Long You, Peter Horsch, Andrzej M. Oleś

We present an exact solution for a class of one-dimensional compass models which stand for interacting orbital degrees of freedom in a Mott insulator. By employing the Jordan-Wigner transformation we map these models on noninteracting fermions and discuss how spin correlations, high degeneracy of the ground state, and ${Z}_{2}$ symmetry in the quantum compass model are visible in the fermionic language. Considering a zigzag chain of ions with singly occupied ${e}_{g}$ orbitals (${e}_{g}$ orbital model) we demonstrate that the orbital excitations change qualitatively with increasing transverse field, and that the excitation gap closes at the quantum phase transition to a polarized state. This phase transition disappears in the quantum compass model with maximally frustrated orbital interactions which resembles the Kitaev model. Here we find that the finite transverse field destabilizes the orbital-liquid ground state with macroscopic degeneracy, and leads to peculiar behavior of the specific heat and orbital susceptibility at finite temperature. We show that the entropy and the cooling rate at finite temperature exhibit quite different behavior near the critical point for these two models.

arXiv:1403.5455•Physical Review B•Mar 31, 2014•29 citations

Quantum coherence in a compass chain under an alternating magnetic field

Wen‐Long You, Yimin Wang, Tian-Cheng Yi +2 more

We investigate quantum phase transitions and quantum coherence in a quantum compass chain under an alternating transverse magnetic field. The model can be analytically solved by the Jordan-Wigner transformation and this solution shows that it is equivalent to a two-component one-dimensional (1D) Fermi gas on a lattice. We explore mutual effects of the staggered magnetic interaction and multisite interactions on the energy spectra and analyze the ground-state phase diagram. We use quantum coherence measures to identify the quantum phase transitions. Our results show that ${l}_{1}$ norm of coherence fails to detect faithfully the quantum critical points separating a gapped phase from a gapless phase, which can be pinpointed exactly by relative entropy of coherence. Jensen-Shannon divergence is somewhat obscure at exception points. We also propose an experimental realization of such a 1D system using superconducting quantum circuits.

arXiv:1806.03337•Physical review. B./Physical review. B•Jun 19, 2018•28 citations

Dynamical quantum phase transition in XY chains with the Dzyaloshinskii-Moriya and XZY–YZX three-site interactions

Kaiyuan Cao, Ming Zhong, Peiqing Tong

We study the dynamical quantum phase transitions (DQPTs) in the XY chains with the Dzyaloshinskii–Moriya interaction and the XZY–YZX type of three-site interaction after a sudden quench. Both the models can be mapped to the spinless free fermion models by the Jordan–Wigner and Bogoliubov transformations with the form H = ∑ k ε k ( η k † η k − 1 2 ) , where the quasiparticle excitation spectra εk may be smaller than 0 for some k and are asymmetrical (εk ≠ ε –k ). It is found that the factors of Loschmidt echo equal 1 for some k corresponding to the quasiparticle excitation spectra of the pre-quench Hamiltonian satisfying εk ⋅ ε –k < 0, when the quench is from the gapless phase. By considering the quench from different ground states, we obtain the conditions for the occurrence of DQPTs for the general XY chains with gapless phase, and find that the DQPTs may not occur in the quench across the quantum phase transitions regardless of whether the quench is from the gapless phase to gapped phase or from the gapped phase to gapless phase. This is different from the DQPTs in the case of quench from the gapped phase to gapped phase, in which the DQPTs will always appear. Moreover, we analyze the different reasons for the absence of DQPTs in the quench from the gapless phase and the gapped phase. The conclusion can also be extended to the general quantum spin chains.

Chinese Physics B•Jan 12, 2022•8 citations
We consider a class of one-dimensional compass models with an XYZ-YZX type of three-site exchange interaction in an external magnetic field. We present the exact solution derived by means of Jordan-Wigner transformation, and study the excitation gap, spin correlations, and establish the phase diagram. Besides the canted antiferromagnetic and polarized phases, the three-site interactions induce two distinct chiral phases, corresponding to gapless spinless-fermion systems having two or four Fermi points. We find that the zzz component of the scalar chirality operator can act as an order parameter for these chiral phases. We also find that the thermodynamic quantities including the Wilson ratio can characterize the liquid phases. Finally, a nontrivial magnetoelectric effect is explored, and we show that the polarization can be manipulated by the magnetic field in the absence of electric field.
We consider a class of one-dimensional compass models with antisymmetric Dzyaloshinskii-Moriya exchange interaction in an external magnetic field. Based on the exact solution derived by means of Jordan-Wigner transformation, we study the excitation gap, spin correlations, ground-state degeneracy, and critical properties at phase transitions. The phase diagram at finite electric and magnetic field consists of three phases: ferromagnetic, canted antiferromagnetic, and chiral. Dzyaloshinskii-Moriya interaction induces an electrical polarization in the ground state of the chiral phase, where the nonlocal string order and special features of entanglement spectra arise, while strong chiral correlations emerge at finite temperature in the other phases and are controlled by a gap between the nonchiral ground state and the chiral excitations. We further show that the magnetoelectric effects in all phases disappear above a typical temperature corresponding to the total bandwidth of the effective fermionic model. To this end we explore the entropy, specific heat, magnetization, electric polarization, and the magnetoelectric tensor at finite temperature. We identify rather peculiar specific-heat and polarization behavior of the compass model which follows from highly frustrated interactions.
We consider a class of one-dimensional compass models with staggered Dzyaloshinskii-Moriya exchange interactions in an external transverse magnetic field. Based on the exact solution derived from Jordan-Wigner approach, we study the excitation gap, energy spectra, spin correlations and critical properties at phase transitions. We explore mutual effects of the staggered Dzyaloshinskii-Moriya interaction and the magnetic field on the energy spectra and the ground-state phase diagram. Thermodynamic quantities including the entropy and the specific heat are discussed, and their universal scalings at low temperature are demonstrated.
Critical Phases of the extended isotropic XYXYXY chain with four-spin interaction
Using the Jordan-Wigner transformation we calculate exactly the ground state and low-temperature thermodynamic properties of the spin S=1/2S=1/2S=1/2 isotropic XXXXXX chain with four spin interaction. In terms of the equivalent spinless fermion (SF) representation the system is viewed as a lattice fermion gas with nearest-neighbor (JJJ) and next-next-next-neighbor (J∗/4J^{\ast}/4J∗/4) hopping. It is shown that with the increase of four spin coupling, at Jc∗=4J/3J^{\ast}_{c} = 4J/3Jc∗​=4J/3 the system experiences the Lifshitz type topological phase transition characterized by the tripling of Fermi points. The quantum phase transition (QPT) point marks transition from a gapless spin-liquid phase of standard XXXXXX chain into again a gapless spin-liquid phase with different character of power-low decay of spin correlations. At the transition point the free fermion dispersion relation shows flattering at Fermi points, what determines singular character of density of states ρ(ω)∼(ω/J)−2/3ρ(ω)\sim (ω/J)^{-2/3}ρ(ω)∼(ω/J)−2/3 and as a consequence unconventional temperature dependence of heat capacity of the system C∼(T/J∗)1/3C\sim (T/J^{\ast})^{1/3}C∼(T/J∗)1/3, and singular magnetic susceptibility of the system χ(H)∼(H/J∗)−2/3χ(H)\sim (H/J^{\ast})^{-2/3}χ(H)∼(H/J∗)−2/3. In the case of alternating magnetic field the system is characterized by the rich ground state phase diagram which contains fully polarized (ferromagnetic), gapped antiferromagnetic (AFM) and spin liquid phases. At the transition point from the gapped AFM phase into the gapless polarized spin liquid phase the system shows rapid increase of magnetization m∼(H−Hc)1/6m\sim(H-H_c)^{1/6}m∼(H−Hc​)1/6 and magnetic susceptibility a singular behavior as χ(H)∼(H−Hc)−5/6χ(H)\sim (H-H_c)^{-5/6}χ(H)∼(H−Hc​)−5/6.
We present an exact solution for a class of one-dimensional compass models which stand for interacting orbital degrees of freedom in a Mott insulator. By employing the Jordan-Wigner transformation we map these models on noninteracting fermions and discuss how spin correlations, high degeneracy of the ground state, and Z2{Z}_{2}Z2​ symmetry in the quantum compass model are visible in the fermionic language. Considering a zigzag chain of ions with singly occupied eg{e}_{g}eg​ orbitals (eg{e}_{g}eg​ orbital model) we demonstrate that the orbital excitations change qualitatively with increasing transverse field, and that the excitation gap closes at the quantum phase transition to a polarized state. This phase transition disappears in the quantum compass model with maximally frustrated orbital interactions which resembles the Kitaev model. Here we find that the finite transverse field destabilizes the orbital-liquid ground state with macroscopic degeneracy, and leads to peculiar behavior of the specific heat and orbital susceptibility at finite temperature. We show that the entropy and the cooling rate at finite temperature exhibit quite different behavior near the critical point for these two models.
We investigate quantum phase transitions and quantum coherence in a quantum compass chain under an alternating transverse magnetic field. The model can be analytically solved by the Jordan-Wigner transformation and this solution shows that it is equivalent to a two-component one-dimensional (1D) Fermi gas on a lattice. We explore mutual effects of the staggered magnetic interaction and multisite interactions on the energy spectra and analyze the ground-state phase diagram. We use quantum coherence measures to identify the quantum phase transitions. Our results show that l1{l}_{1}l1​ norm of coherence fails to detect faithfully the quantum critical points separating a gapped phase from a gapless phase, which can be pinpointed exactly by relative entropy of coherence. Jensen-Shannon divergence is somewhat obscure at exception points. We also propose an experimental realization of such a 1D system using superconducting quantum circuits.
We study the dynamical quantum phase transitions (DQPTs) in the XY chains with the Dzyaloshinskii–Moriya interaction and the XZY–YZX type of three-site interaction after a sudden quench. Both the models can be mapped to the spinless free fermion models by the Jordan–Wigner and Bogoliubov transformations with the form H = ∑ k ε k ( η k † η k − 1 2 ) , where the quasiparticle excitation spectra εk may be smaller than 0 for some k and are asymmetrical (εk ≠ ε –k ). It is found that the factors of Loschmidt echo equal 1 for some k corresponding to the quasiparticle excitation spectra of the pre-quench Hamiltonian satisfying εk ⋅ ε –k < 0, when the quench is from the gapless phase. By considering the quench from different ground states, we obtain the conditions for the occurrence of DQPTs for the general XY chains with gapless phase, and find that the DQPTs may not occur in the quench across the quantum phase transitions regardless of whether the quench is from the gapless phase to gapped phase or from the gapped phase to gapless phase. This is different from the DQPTs in the case of quench from the gapped phase to gapped phase, in which the DQPTs will always appear. Moreover, we analyze the different reasons for the absence of DQPTs in the quench from the gapless phase and the gapped phase. The conclusion can also be extended to the general quantum spin chains.