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:1910.09733 · Physical review. B./Physical review. B

Quantum Lifshitz criticality in a frustrated two-dimensional XY model

Yaroslav A. Kharkov, J. Oitmaa, Oleg P. Sushkov

Published Jan 9, 2020• 5 citations
arXivHTMLPDF

Abstract

Antiferromagnetic quantum spin systems can exhibit a transition between collinear and spiral ground states, driven by frustration. Classically this is a smooth crossover and the crossover point is termed a Lifshitz point. Quantum fluctuations change the nature of the transition. In particular, it has been argued previously that in the two-dimensional (2D) case a spin liquid (SL) state is developed in the vicinity of the Lifshitz point, termed a Lifshitz SL. In the present work, using a field theory approach, we solve the Lifshitz quantum phase transition problem for the 2D frustrated XY model. Specifically, we show that, unlike the $SU(2)$ symmetric Lifshitz case, in the XY model, the SL exists only at the critical point. At zero temperature we calculate nonuniversal critical exponents in the N\'eel and in the spin spiral state and relate these to properties of the SL. We also solve the transition problem at a finite temperature and discuss the role of topological excitations.

DOI
10.1103/physrevb.101.035114

Related papers

Vector Chiral Phases in the Frustrated 2D X Y Model and Quantum Spin Chains

H. Schenck, V. L. Pokrovsky, Thomas Nattermann

The phase diagram of the frustrated 2D classical and 1D quantum XY models is calculated analytically. Four transitions are found: the vortex unbinding transitions triggered by strong fluctuations occur above and below the chiral transition temperature. Vortex interaction is short range on small and logarithmic on large scales. The chiral transition, though belonging to the Ising universality class by symmetry, has different critical exponents due to nonlocal interaction. In a narrow region close to the Lifshitz point a reentrant phase transition between paramagnetic and quasiferromagnetic phase appears. Applications to antiferromagnetic quantum spin chains and multiferroics are discussed.

arXiv:1308.0823•Physical Review Letters•Apr 14, 2014•12 citations

Quantum destruction of spiral order in two-dimensional frustrated magnets

Subhro Bhattacharjee

We study the fate of spin-$1/2$ spiral-ordered two-dimensional quantum antiferromagnets that are disordered by quantum fluctuations. A crucial role is played by the topological point defects of the spiral phase, which are known to have a ${Z}_{2}$ character. Previous works established that a nontrivial quantum spin-liquid phase results when the spiral is disordered without proliferating the ${Z}_{2}$ vortices. Here, we show that when the spiral is disordered by proliferating and condensing these vortices, valence-bond solid ordering occurs due to quantum Berry phase effects. We develop a general theory for this latter phase transition and apply it to a lattice model. This transition potentially provides a new example of a Landau-forbidden deconfined quantum critical point.

arXiv:1011.4827•Physical Review B•Sep 15, 2011•9 citations

Colossal quasiparticle radiation in the Lifshitz spin liquid phase of a two-dimensional quantum antiferromagnet

Matthew C. O'Brien, Oleg P. Sushkov

Strong quantum fluctuations in magnetic systems can create disordered quantum spin liquid phases of matter which are not predicted by classical physics. The complexity of the exotic phenomena on display in spin liquids has led to a great deal of theoretical and experimental interest. However, understanding the fundamental nature of the excitations in these systems remains challenging. In this work, we consider the Lifshitz quantum critical point in a two-dimensional frustrated $XY$ antiferromagnet. At this point, quantum fluctuations destroy long-range order, leading to the formation of an algebraic Lifshitz spin liquid. We demonstrate that the bosonic magnon excitations are long-lived and well-defined in the Lifshitz spin liquid phase, though paradoxically, the dynamic structure factor has a broad non-Lorentzian frequency distribution with no single-particle weight. We resolve this apparent contradiction by showing that the Lifshitz spin liquid suffers from an infrared catastrophe: An external physical probe always excites an infinite number of arbitrarily low-energy quasiparticles, which leads to significant radiative broadening of the spectrum.

arXiv:2003.03936•Physical review. B./Physical review. B•May 7, 2020•3 citations

Phase diagrams of two-dimensional frustrated spin systems

Ansgar Kalz

In this work the ordering processes in classical frustrated Ising models and the ground-state behavior of frustrated quantum spin models are investigated. In the first part the phase transition from a high-temperature paramagnetic phase to a antiferromagnetic ground state is analyzed for the square-lattice Ising model with competing antiferromagnetic interactions between nearest- and next-nearest-neighbor spins. In the case of spatially isotropic interactions the phase transition to a collinear state is of special interest. Using Monte-Carlo simulations on finite lattices as well as field-theoretical methods for the continuous model it is shown that depending on the frustration three different sectors can be distinguished that show (i) Ising-universal behavior (ii) Ashkin-Teller-like non-universal behavior (varying critical exponents) and (iii) non-critical first-order behavior. For spatially anisotropic interactions the emergence of an intermediate incommensurate phase is verified by means of Monte-Carlo simulations which has been predicted by earlier mean-field calculations. The nature of this phase is studied analyzing spin-spin correlation functions and its ordering wave-vector reveals a strong temperature and size dependence. In the second part the influence of quantum fluctuations on classical antiferromagnetic ground states are investigated in anisotropic quantum spin-1/2 Heisenberg models with competing interactions. Using quantum Monte-Carlo simulations, exact diagonalization and perturbation theory the ground-state phase diagrams are calculated for a square lattice with nearest- and next-nearest-neighbor interactions and a honeycomb lattice with up to third-nearest-neighbor interactions whereby the fluctuations are chosen to be non-frustrating. For both cases the stability regions of classical magnetic states are identified and an intermediate phase is detected that shows no sign of long-range magnetic order. Further calculations also rule out valence-bond-crystal or topological order for this state, thus a quantum disordered ground state is stabilized in these models.

•Jan 1, 2012•0 citations

Critical exponents of the fully frustrated two-dimensionalXYmodel

Guillermo Ramı́rez-Santiago, Jorge V. José

We present a detailed study of the critical properties of the two-dimensional (2D) XY model with maximal frustration in a square lattice. We use extensive Monte Carlo simulations to study the thermodynamics of the spin and chiral degrees of freedom, concentrating on their correlation functions. The gauge-invariant spin-spin correlation functions are calculated close to the critical point for lattice sizes up to 240\ifmmode\times\else\texttimes\fi{}240; the chiral correlation functions are studied on lattices up to 96\ifmmode\times\else\texttimes\fi{}96. We find that the critical exponents of the spin-phase transition are \ensuremath{\nu}=0.3069 and \ensuremath{\eta}=0.1915, which are to be compared with the unfrustrated XY model exponents \ensuremath{\nu}=1/2 and \ensuremath{\eta}=0.25. We also find that the critical exponents of the chiral transition are ${\ensuremath{\nu}}_{\mathrm{\ensuremath{\chi}}}$=0.875, 2\ensuremath{\beta}=0.1936, 2\ensuremath{\gamma}=1.82, and 2\ensuremath{\gamma}'=1.025, which are different from the expected 2D Ising critical exponents. The spin-phase transition occurs at ${\mathit{T}}_{\mathit{U}(1)}$=0.446, which is about 7% above the estimated chiral critical temperature ${\mathit{T}}_{\mathit{Z}2}$=0.4206. However, because of the size of the statistical errors, it is difficult to decide with certainty whether the transitions occur at the same or at slightly different temperatures. Finally, the jump in the helicity modulus in the fully frustrated system is found to be about 23% below the unfrustrated universal value. The most important consequence of these results is that the fully frustrated XY model appears to be in a novel universality class. Recent successful comparisons of some of these results with experimental data are also briefly discussed.

arXiv:cond-mat/9402100•Physical review. B, Condensed matter•Apr 1, 1994•87 citations

Critical behavior of two-dimensional fully frustrated XY systems

Martin Hasenbusch, Andrea Pelissetto, Ettore Vicari

We study the phase diagram of the two-dimensional fully frustrated XY model (FFXY) and of two related models, a lattice discretization of the Landau-Ginzburg-Wilson Hamiltonian for the critical modes of the FFXY model, and a coupled Ising-XY model. We present Monte Carlo simulations on square lattices L × L , L ≲ 10 3 . We show that the low-temperature phase of these models is controlled by the same line of Gaussian fixed points as in the standard XY model. We find that, if a model undergoes a unique transition by varying temperature, then the transition is of first order. In the opposite case we observe two very close transitions: a transition associated with the spin degrees of freedom and, as temperature increases, a transition where chiral modes become critical. If they are continuous, they belong to the Kosterlitz-Thouless and to the Ising universality class, respectively. Ising and Kosterlitz-Thouless behavior is observed only after a preasymptotic regime, which is universal to some extent. In the chiral case, the approach is nonmonotonic for most observables, and there is a wide region in which finite-size scaling is controlled by an effective exponent ν eff ≈ 0.8. This explains the result ν ≈ 0.8 of many previous studies using smaller lattices.

arXiv:cond-mat/0509511•Journal of Physics Conference Series•Jun 1, 2006•4 citations
Antiferromagnetic quantum spin systems can exhibit a transition between collinear and spiral ground states, driven by frustration. Classically this is a smooth crossover and the crossover point is termed a Lifshitz point. Quantum fluctuations change the nature of the transition. In particular, it has been argued previously that in the two-dimensional (2D) case a spin liquid (SL) state is developed in the vicinity of the Lifshitz point, termed a Lifshitz SL. In the present work, using a field theory approach, we solve the Lifshitz quantum phase transition problem for the 2D frustrated XY model. Specifically, we show that, unlike the SU(2)SU(2)SU(2) symmetric Lifshitz case, in the XY model, the SL exists only at the critical point. At zero temperature we calculate nonuniversal critical exponents in the N'eel and in the spin spiral state and relate these to properties of the SL. We also solve the transition problem at a finite temperature and discuss the role of topological excitations.
The phase diagram of the frustrated 2D classical and 1D quantum XY models is calculated analytically. Four transitions are found: the vortex unbinding transitions triggered by strong fluctuations occur above and below the chiral transition temperature. Vortex interaction is short range on small and logarithmic on large scales. The chiral transition, though belonging to the Ising universality class by symmetry, has different critical exponents due to nonlocal interaction. In a narrow region close to the Lifshitz point a reentrant phase transition between paramagnetic and quasiferromagnetic phase appears. Applications to antiferromagnetic quantum spin chains and multiferroics are discussed.
We study the fate of spin-1/21/21/2 spiral-ordered two-dimensional quantum antiferromagnets that are disordered by quantum fluctuations. A crucial role is played by the topological point defects of the spiral phase, which are known to have a Z2{Z}_{2}Z2​ character. Previous works established that a nontrivial quantum spin-liquid phase results when the spiral is disordered without proliferating the Z2{Z}_{2}Z2​ vortices. Here, we show that when the spiral is disordered by proliferating and condensing these vortices, valence-bond solid ordering occurs due to quantum Berry phase effects. We develop a general theory for this latter phase transition and apply it to a lattice model. This transition potentially provides a new example of a Landau-forbidden deconfined quantum critical point.
Strong quantum fluctuations in magnetic systems can create disordered quantum spin liquid phases of matter which are not predicted by classical physics. The complexity of the exotic phenomena on display in spin liquids has led to a great deal of theoretical and experimental interest. However, understanding the fundamental nature of the excitations in these systems remains challenging. In this work, we consider the Lifshitz quantum critical point in a two-dimensional frustrated XYXYXY antiferromagnet. At this point, quantum fluctuations destroy long-range order, leading to the formation of an algebraic Lifshitz spin liquid. We demonstrate that the bosonic magnon excitations are long-lived and well-defined in the Lifshitz spin liquid phase, though paradoxically, the dynamic structure factor has a broad non-Lorentzian frequency distribution with no single-particle weight. We resolve this apparent contradiction by showing that the Lifshitz spin liquid suffers from an infrared catastrophe: An external physical probe always excites an infinite number of arbitrarily low-energy quasiparticles, which leads to significant radiative broadening of the spectrum.
In this work the ordering processes in classical frustrated Ising models and the ground-state behavior of frustrated quantum spin models are investigated. In the first part the phase transition from a high-temperature paramagnetic phase to a antiferromagnetic ground state is analyzed for the square-lattice Ising model with competing antiferromagnetic interactions between nearest- and next-nearest-neighbor spins. In the case of spatially isotropic interactions the phase transition to a collinear state is of special interest. Using Monte-Carlo simulations on finite lattices as well as field-theoretical methods for the continuous model it is shown that depending on the frustration three different sectors can be distinguished that show (i) Ising-universal behavior (ii) Ashkin-Teller-like non-universal behavior (varying critical exponents) and (iii) non-critical first-order behavior. For spatially anisotropic interactions the emergence of an intermediate incommensurate phase is verified by means of Monte-Carlo simulations which has been predicted by earlier mean-field calculations. The nature of this phase is studied analyzing spin-spin correlation functions and its ordering wave-vector reveals a strong temperature and size dependence. In the second part the influence of quantum fluctuations on classical antiferromagnetic ground states are investigated in anisotropic quantum spin-1/2 Heisenberg models with competing interactions. Using quantum Monte-Carlo simulations, exact diagonalization and perturbation theory the ground-state phase diagrams are calculated for a square lattice with nearest- and next-nearest-neighbor interactions and a honeycomb lattice with up to third-nearest-neighbor interactions whereby the fluctuations are chosen to be non-frustrating. For both cases the stability regions of classical magnetic states are identified and an intermediate phase is detected that shows no sign of long-range magnetic order. Further calculations also rule out valence-bond-crystal or topological order for this state, thus a quantum disordered ground state is stabilized in these models.
We present a detailed study of the critical properties of the two-dimensional (2D) XY model with maximal frustration in a square lattice. We use extensive Monte Carlo simulations to study the thermodynamics of the spin and chiral degrees of freedom, concentrating on their correlation functions. The gauge-invariant spin-spin correlation functions are calculated close to the critical point for lattice sizes up to 240\ifmmode\times\else\texttimes\fi{}240; the chiral correlation functions are studied on lattices up to 96\ifmmode\times\else\texttimes\fi{}96. We find that the critical exponents of the spin-phase transition are \ensuremath{\nu}=0.3069 and \ensuremath{\eta}=0.1915, which are to be compared with the unfrustrated XY model exponents \ensuremath{\nu}=1/2 and \ensuremath{\eta}=0.25. We also find that the critical exponents of the chiral transition are ${\ensuremath{\nu}}_{\mathrm{\ensuremath{\chi}}}$=0.875, 2\ensuremath{\beta}=0.1936, 2\ensuremath{\gamma}=1.82, and 2\ensuremath{\gamma}'=1.025, which are different from the expected 2D Ising critical exponents. The spin-phase transition occurs at TU(1){\mathit{T}}_{\mathit{U}(1)}TU(1)​=0.446, which is about 7% above the estimated chiral critical temperature TZ2{\mathit{T}}_{\mathit{Z}2}TZ2​=0.4206. However, because of the size of the statistical errors, it is difficult to decide with certainty whether the transitions occur at the same or at slightly different temperatures. Finally, the jump in the helicity modulus in the fully frustrated system is found to be about 23% below the unfrustrated universal value. The most important consequence of these results is that the fully frustrated XY model appears to be in a novel universality class. Recent successful comparisons of some of these results with experimental data are also briefly discussed.
We study the phase diagram of the two-dimensional fully frustrated XY model (FFXY) and of two related models, a lattice discretization of the Landau-Ginzburg-Wilson Hamiltonian for the critical modes of the FFXY model, and a coupled Ising-XY model. We present Monte Carlo simulations on square lattices L × L , L ≲ 10 3 . We show that the low-temperature phase of these models is controlled by the same line of Gaussian fixed points as in the standard XY model. We find that, if a model undergoes a unique transition by varying temperature, then the transition is of first order. In the opposite case we observe two very close transitions: a transition associated with the spin degrees of freedom and, as temperature increases, a transition where chiral modes become critical. If they are continuous, they belong to the Kosterlitz-Thouless and to the Ising universality class, respectively. Ising and Kosterlitz-Thouless behavior is observed only after a preasymptotic regime, which is universal to some extent. In the chiral case, the approach is nonmonotonic for most observables, and there is a wide region in which finite-size scaling is controlled by an effective exponent ν eff ≈ 0.8. This explains the result ν ≈ 0.8 of many previous studies using smaller lattices.