Deconfined classical criticality in the anisotropic quantum spin- 1 2 XY model on the square lattice

Mudry, Christopher; Aksoy, Ömer M.; Chamon, Claudio; Furusaki, Akira

doi:10.1103/PhysRevB.111.104402

Deconfined classical criticality in the anisotropic quantum spin- $\frac{1}{2}$ XY model on the square lattice

Journal Article · Sun Mar 02 23:00:00 EST 2025 · Physical Review. B

DOI:https://doi.org/10.1103/PhysRevB.111.104402· OSTI ID:2526289

; Aksoy, Ömer M.; ;

The anisotropic quantum spin- $\frac{1}{2}$ XY model on a linear chain was solved by Lieb, Schultz, and Mattis [] and shown to display a continuous quantum phase transition at the O(2) symmetric point separating two gapped phases with competing Ising long-range order. For the square lattice, the following is known. The two competing Ising ordered phases extend to finite temperatures, up to a boundary where a transition to the paramagnetic phase occurs, and meet at the O(2) symmetric critical line along the temperature axis that ends at a tricritical point at the Berezinskii-Kosterlitz-Thouless transition temperature where the two competing phases meet the paramagnetic phase. We show that the first-order zero-temperature (quantum) phase transition that separates the competing phases as a function of the anisotropy parameter is smoothed by thermal fluctuations into deconfined classical criticality.

Published by the American Physical Society 2025

View Journal Article

Sponsoring Organization:: USDOE

Grant/Contract Number:: FG02-06ER46316

OSTI ID:: 2526289

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 10 Vol. 111; ISSN 2469-9950; ISSN PRBMDO

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (67)

Phase transitions in anisotropic two‐dimensional quantum antiferromagnets Roscilde, T.; Cuccoli, A.; Verrucchi, P. physica status solidi (b), Vol. 236, Issue 2 https://doi.org/10.1002/pssb.200301697	journal	March 2003
Finite size and temperature effects in the AF Heisenberg model Hasenfratz, P.; Niedermayer, F. Zeitschrift f�r Physik B Condensed Matter, Vol. 92, Issue 1 https://doi.org/10.1007/BF01309171	journal	March 1993
Thermodynamics of the two-dimensional spin-1/2 XY model De Readt, H.; De Raedt, B.; Lagendijk, A. Zeitschrift für Physik B Condensed Matter, Vol. 57, Issue 3 https://doi.org/10.1007/BF01318413	journal	September 1984
�ber das Paulische �quivalenzverbot Jordan, P.; Wigner, E. Zeitschrift f�r Physik, Vol. 47, Issue 9-10 https://doi.org/10.1007/BF01331938	journal	September 1928
Field theories with « Superconductor » solutions Goldstone, J. Il Nuovo Cimento, Vol. 19, Issue 1 https://doi.org/10.1007/BF02812722	journal	January 1961
Beitrag zur Theorie des Ferromagnetismus Ising, Ernst Zeitschrift für Physik, Vol. 31, Issue 1 https://doi.org/10.1007/BF02980577	journal	February 1925
Two soluble models of an antiferromagnetic chain Lieb, Elliott; Schultz, Theodore; Mattis, Daniel Annals of Physics, Vol. 16, Issue 3 https://doi.org/10.1016/0003-4916(61)90115-4	journal	December 1961
Monte Carlo simulations of the two-dimensional quantal and classical spin systems — A new type of phase transition with vortices Suzuki, Masuo; Miyashita, Seiji; Kuroda, Akira Physics Letters A, Vol. 60, Issue 5 https://doi.org/10.1016/0375-9601(77)90061-5	journal	March 1977
On the ground state of the XY magnet and Heisenberg antiferromagnet on the square lattice Betts, D. D.; Oitmaa, J. Physics Letters A, Vol. 62, Issue 4 https://doi.org/10.1016/0375-9601(77)90796-4	journal	August 1977
Ground state properties of the Heisenberg antiferromagnet and XY magnet in three dimensions Oitmaa, J.; Betts, D. D. Physics Letters A, Vol. 68, Issue 5-6 https://doi.org/10.1016/0375-9601(78)90625-4	journal	October 1978
Susceptibilities of the model on the square lattice at T = 0 Oitmaa, J.; Betts, D. D.; Marland, L. G. Physics Letters A, Vol. 79, Issue 2-3 https://doi.org/10.1016/0375-9601(80)90245-5	journal	September 1980
Monte Carlo study of the two-dimensional spin-1/2 XY model De Raedt, Hans; De Raedt, Bart; Fivez, Jan Physics Letters A, Vol. 104, Issue 8 https://doi.org/10.1016/0375-9601(84)90750-3	journal	September 1984
Zero-temperature ordering in the two-dimensional quantum XY model Tang, Sanyee Physics Letters A, Vol. 129, Issue 2 https://doi.org/10.1016/0375-9601(88)90074-6	journal	May 1988
Real space renormalization group study of the anisotropic quantum Heisenberg model on a square lattice Drzewinski, A.; Sznajd, J. Physics Letters A, Vol. 138, Issue 3 https://doi.org/10.1016/0375-9601(89)90880-3	journal	June 1989
Quantum effects in the 2D XY model Schindelin, C.; Fehske, H.; Büttner, H. Journal of Magnetism and Magnetic Materials, Vol. 226-230 https://doi.org/10.1016/S0304-8853(00)01193-8	journal	May 2001
The spin-half XXZ antiferromagnet on the square lattice revisited: A high-order coupled cluster treatment Bishop, R. F.; Li, P. H. Y.; Zinke, R. Journal of Magnetism and Magnetic Materials, Vol. 428 https://doi.org/10.1016/j.jmmm.2016.11.043	journal	April 2017
(Pseudo-)Goldstone boson interaction in D = 2 + 1 systems with a spontaneously broken internal rotation symmetry Hofmann, Christoph P. Nuclear Physics B, Vol. 904 https://doi.org/10.1016/j.nuclphysb.2016.01.018	journal	March 2016
On Ising's model of ferromagnetism Peierls, R. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 32, Issue 3 https://doi.org/10.1017/S0305004100019174	journal	October 1936
Ordering, metastability and phase transitions in two-dimensional systems Kosterlitz, J M; Thouless, D J Journal of Physics C: Solid State Physics, Vol. 6, Issue 7, p. 1181-1203 https://doi.org/10.1088/0022-3719/6/7/010	journal	April 1973
Monte Carlo Simulations of the Quantum X-Y Model by a Loop-Cluster Algorithm Ji, Daren; Ying, Heping Chinese Physics Letters, Vol. 11, Issue 1 https://doi.org/10.1088/0256-307X/11/1/014	journal	January 1994
Finite-size scaling in the spin- model on a square lattice Hamer, C. J.; Hövelborn, Tobias; Bachhuber, Michael Journal of Physics A: Mathematical and General, Vol. 32, Issue 1 https://doi.org/10.1088/0305-4470/32/1/007	journal	January 1999
Quantum Monte Carlo analysis of the 2D Heisenberg antiferromagnet withS=1/2: the influence of exchange anisotropy Aplesnin, S. S. Journal of Physics: Condensed Matter, Vol. 10, Issue 44 https://doi.org/10.1088/0953-8984/10/44/012	journal	November 1998
Antiferromagnetic transitions in high-T _c materials Ding, H. -Q Journal of Physics: Condensed Matter, Vol. 2, Issue 39 https://doi.org/10.1088/0953-8984/2/39/010	journal	October 1990
Systematic effective field theory analysis of the D=2+1 quantum XY model at low temperatures Hofmann, Christoph P. Journal of Statistical Mechanics: Theory and Experiment, Vol. 2014, Issue 2 https://doi.org/10.1088/1742-5468/2014/02/P02006	journal	February 2014
Quasi-Particles and Gauge Invariance in the Theory of Superconductivity Nambu, Yoichiro Physical Review, Vol. 117, Issue 3 https://doi.org/10.1103/PhysRev.117.648	journal	February 1960
Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition Onsager, Lars Physical Review, Vol. 65, Issue 3-4 https://doi.org/10.1103/PhysRev.65.117	journal	February 1944
Superfluid to normal phase transition in strongly correlated bosons in two and three dimensions Carrasquilla, Juan; Rigol, Marcos Physical Review A, Vol. 86, Issue 4 https://doi.org/10.1103/PhysRevA.86.043629	journal	October 2012
Quantum renormalization group of theXYmodel in two dimensions Usman, M.; Ilyas, Asif; Khan, Khalid Physical Review A, Vol. 92, Issue 3 https://doi.org/10.1103/PhysRevA.92.032327	journal	September 2015
Estimates of the ground-state eigenvalue of the two-dimensional spin-12X−Ymodel Pearson, Robert B. Physical Review B, Vol. 16, Issue 3 https://doi.org/10.1103/PhysRevB.16.1109	journal	August 1977
Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model José, Jorge V.; Kadanoff, Leo P.; Kirkpatrick, Scott Physical Review B, Vol. 16, Issue 3 https://doi.org/10.1103/PhysRevB.16.1217	journal	August 1977
Monte Carlo studies of the quantumXYmodel in two dimensions Loh, E.; Scalapino, D. J.; Grant, P. M. Physical Review B, Vol. 31, Issue 7 https://doi.org/10.1103/PhysRevB.31.4712	journal	April 1985
Application of spin-wave theory to the ground state ofXYquantum Hamiltonians Gomez-Santos, G.; Joannopoulos, J. D. Physical Review B, Vol. 36, Issue 16 https://doi.org/10.1103/PhysRevB.36.8707	journal	December 1987
Two-dimensional quantum Heisenberg antiferromagnet at low temperatures Chakravarty, Sudip; Halperin, Bertrand I.; Nelson, David R. Physical Review B, Vol. 39, Issue 4 https://doi.org/10.1103/PhysRevB.39.2344	journal	February 1989
Evidence for a phase transition in the zero-temperature anisotropic two-dimensional Heisenberg antiferromagnet Barnes, T.; Kotchan, D.; Swanson, E. S. Physical Review B, Vol. 39, Issue 7 https://doi.org/10.1103/PhysRevB.39.4357	journal	March 1989
Kosterlitz-Thouless transition in the two-dimensional quantumXYmodel Ding, H. -Q.; Makivić, M. S. Physical Review B, Vol. 42, Issue 10 https://doi.org/10.1103/PhysRevB.42.6827	journal	October 1990
Zero-temperature properties of the quantumXYmodel with anisotropy Hamer, C. J.; Oitmaa, J. Physical Review B, Vol. 43, Issue 13 https://doi.org/10.1103/PhysRevB.43.10789	journal	May 1991
Green’s-function Monte Carlo study of the two-dimensional, spin-1/2XYferromagnet Zhang, Shiwei; Runge, Karl J. Physical Review B, Vol. 45, Issue 2 https://doi.org/10.1103/PhysRevB.45.1052	journal	January 1992
Phase transition and thermodynamics of quantumXYmodel in two dimensions Ding, H. -Q. Physical Review B, Vol. 45, Issue 1 https://doi.org/10.1103/PhysRevB.45.230	journal	January 1992
Low temperature phase of the two-dimensional quantumXYmodel Makivic´, M. S. Physical Review B, Vol. 46, Issue 5 https://doi.org/10.1103/PhysRevB.46.3167	journal	August 1992
Low-temperature thermodynamic study of theXYmodel using a self-consistent harmonic approximation Pires, A. S. T. Physical Review B, Vol. 53, Issue 1 https://doi.org/10.1103/PhysRevB.53.235	journal	January 1996
Ground-state parameters, finite-size scaling, and low-temperature properties of the two-dimensional S = 1 2 XY model Sandvik, Anders W.; Hamer, Chris J. Physical Review B, Vol. 60, Issue 9 https://doi.org/10.1103/PhysRevB.60.6588	journal	September 1999
Exact diagonalization and quantum Monte Carlo study of the spin-12XXZmodel on the square lattice Lin, H. -Q.; Flynn, J. S.; Betts, D. D. Physical Review B, Vol. 64, Issue 21 https://doi.org/10.1103/PhysRevB.64.214411	journal	November 2001
Quantum Monte Carlo study of S = 1 2 weakly anisotropic antiferromagnets on the square lattice Cuccoli, Alessandro; Roscilde, Tommaso; Tognetti, Valerio Physical Review B, Vol. 67, Issue 10 https://doi.org/10.1103/PhysRevB.67.104414	journal	March 2003
Aspect-ratio dependence of the spin stiffness of a two-dimensional XY model Melko, R. G.; Sandvik, A. W.; Scalapino, D. J. Physical Review B, Vol. 69, Issue 1 https://doi.org/10.1103/PhysRevB.69.014509	journal	January 2004
One-dimensional symmetry protected topological phases and their transitions Verresen, Ruben; Moessner, Roderich; Pollmann, Frank Physical Review B, Vol. 96, Issue 16 https://doi.org/10.1103/PhysRevB.96.165124	journal	October 2017
Topological phase transition of the anisotropic XY model with Dzyaloshinskii-Moriya interaction Farajollahpour, T.; Jafari, S. A. Physical Review B, Vol. 98, Issue 8 https://doi.org/10.1103/PhysRevB.98.085136	journal	August 2018
Ising ferromagnet to valence bond solid transition in a one-dimensional spin chain: Analogies to deconfined quantum critical points Jiang, Shenghan; Motrunich, Olexei Physical Review B, Vol. 99, Issue 7 https://doi.org/10.1103/PhysRevB.99.075103	journal	February 2019
Quantum phase transitions beyond Landau-Ginzburg theory in one-dimensional space revisited Mudry, Christopher; Furusaki, Akira; Morimoto, Takahiro Physical Review B, Vol. 99, Issue 20 https://doi.org/10.1103/PhysRevB.99.205153	journal	May 2019
Existence of Phase Transitions for Anisotropic Heisenberg Models Fröhlich, Jürg; Lieb, Elliott H. Physical Review Letters, Vol. 38, Issue 8 https://doi.org/10.1103/PhysRevLett.38.440	journal	February 1977
The XY Model Has Long-Range Order for All Spins and All Dimensions Greater than One Kennedy, Tom; Lieb, Elliott H.; Shastry, B. Sriram Physical Review Letters, Vol. 61, Issue 22 https://doi.org/10.1103/PhysRevLett.61.2582	journal	November 1988
Existence of Long-Range Order in the XXZ Model Kubo, Kenn; Kishi, Tatsuya Physical Review Letters, Vol. 61, Issue 22 https://doi.org/10.1103/PhysRevLett.61.2585	journal	November 1988
Could in-plane exchange anisotropy induce the observed antiferromagnetic transitions in the undoped high- T c materials? Ding, H. -Q. Physical Review Letters, Vol. 68, Issue 12 https://doi.org/10.1103/PhysRevLett.68.1927	journal	March 1992
The spin-½ Heisenberg antiferromagnet on a square lattice and its application to the cuprous oxides Manousakis, Efstratios Reviews of Modern Physics, Vol. 63, Issue 1 https://doi.org/10.1103/RevModPhys.63.1	journal	January 1991
The spin model. I. Derivation of high temperature series expansions for thermodynamic quantities Rogiers, J.; Lookman, T.; Betts, D. D. Canadian Journal of Physics, Vol. 56, Issue 4 https://doi.org/10.1139/p78-053	journal	April 1978
The spin model. II. Analysis of high temperature series expansions of some thermodynamic quantities in three dimensions Rogiers, J.; Betts, D. D.; Lookman, T. Canadian Journal of Physics, Vol. 56, Issue 4 https://doi.org/10.1139/p78-054	journal	April 1978
The ground state of two quantum models of magnetism Oitmaa, J.; Betts, D. D. Canadian Journal of Physics, Vol. 56, Issue 7 https://doi.org/10.1139/p78-120	journal	July 1978
Variational study on the ground state of the spin XY magnet Suzuki, Masuo; Miyashita, Seiji Canadian Journal of Physics, Vol. 56, Issue 7 https://doi.org/10.1139/p78-121	journal	July 1978
Renormalization-group approach to quantum Fisher information in the two-dimensional XY model Zhao, Z. J.; Gao, G. J.; Ren, Y. P. The European Physical Journal Plus, Vol. 136, Issue 11 https://doi.org/10.1140/epjp/s13360-021-02152-x	journal	November 2021
Dynamic Monte Carlo Study of the Two-Dimensional Quantum XY Model Ying, H. P.; Luo, H. J.; Schülke, L. Modern Physics Letters B, Vol. 12, Issue 29n30 https://doi.org/10.1142/S0217984998001463	journal	December 1998
Spin Wave Theory of the Spin 1/2 XY Model Uchinami, Mamoru; Takada, Satoshi; Takano, Fumihiko Journal of the Physical Society of Japan, Vol. 47, Issue 4 https://doi.org/10.1143/JPSJ.47.1047	journal	October 1979
Quantum Monte Carlo Simulation of the Spin 1/2XXZModel on the Square Lattice Okabe, Yutaka; Kikuchi, Macoto Journal of the Physical Society of Japan, Vol. 57, Issue 12 https://doi.org/10.1143/JPSJ.57.4351	journal	December 1988
Long-Range Order in Antiferromagnetic Quantum Spin Systems Ozeki, Yukiyasu; Nishimori, Hidetoshi; Tomita, Yasuhiro Journal of the Physical Society of Japan, Vol. 58, Issue 1 https://doi.org/10.1143/JPSJ.58.82	journal	January 1989
Kosterlitz-Thouless Transition of QuantumXYModel in Two Dimensions Harada, Kenji; Kawashima, Naoki Journal of the Physical Society of Japan, Vol. 67, Issue 8 https://doi.org/10.1143/JPSJ.67.2768	journal	August 1998
A Lattice Model of Liquid Helium Matsubara, Takeo; Matsuda, Hirotsugu Progress of Theoretical Physics, Vol. 16, Issue 4 https://doi.org/10.1143/PTP.16.416	journal	October 1956
Quantum Heisenberg Ferromagnets in One and Two Dimensions at Low Temperature Takahashi, Minoru Progress of Theoretical Physics Supplement, Vol. 87 https://doi.org/10.1143/PTPS.87.233	journal	January 1986
Renormalization of trace distance and multipartite entanglement close to the quantum phase transitions of one- and two-dimensional spin-chain systems Wu, Wei; Xu, Jing-Bo EPL (Europhysics Letters), Vol. 115, Issue 4 https://doi.org/10.1209/0295-5075/115/40006	journal	August 2016
Lieb-Schultz-Mattis anomalies and web of dualities induced by gauging in quantum spin chains Aksoy, Ömer Mert; Mudry, Christopher; Furusaki, Akira SciPost Physics, Vol. 16, Issue 1 https://doi.org/10.21468/SciPostPhys.16.1.022	journal	January 2024

Similar Records

Phase diagram of generalized XY model using the tensor renormalization group

Journal Article · Tue Aug 06 00:00:00 EDT 2024 · Physical Review. D. · OSTI ID:2427028

Analog

B (M 1)

strengths in the

T_{z} = \pm \frac{3}{2}

mirror nuclei

{}^{47}{Mn}

and

{}^{47}{Ti}

Journal Article · Thu Apr 04 00:00:00 EDT 2024 · Physical Review. C · OSTI ID:2333698

Entanglement entropy of (

2 + 1

)-dimensional SU(2) lattice gauge theory on plaquette chains

Journal Article · Tue Jul 09 00:00:00 EDT 2024 · Physical Review. D. · OSTI ID:2396396

Deconfined classical criticality in the anisotropic quantum spin- 1 2 XY model on the square lattice

Citation Formats

References (67)

Similar Records

Related Subjects

Deconfined classical criticality in the anisotropic quantum spin- $\frac{1}{2}$ XY model on the square lattice