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 Letters

Ground States of Low-Dimensional Quantum Antiferromagnets

Rajiv R. P. Singh, Martin P. Gelfand, David A. Huse

Published Nov 21, 1988• 128 citations
Publisher

Abstract

We have developed a general scheme for carrying out systematic perturbation expansions for groundstate properties of quantum lattice models. As an application, we study the onset of spontaneous N\'eel order in $S=\frac{1}{2}$ Heisenberg antiferromagnets by expanding around dimerized Hamiltonians. In one dimension (1D) we recover accurately the known exact results. On the square lattice we find novel critical points separating N\'eel ordered and disordered phases; the estimated critical exponents are consistent with those of the 3D classical Heisenberg model.

DOI
10.1103/physrevlett.61.2484

Related papers

Ground state phases of the spin-1/2 J1–J2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment

R. Darradi, Oleg Derzhko, Ronald Zinke +3 more

Using the coupled cluster method for high orders of approximation and complementary exact diagonalization studies we investigate the ground state properties of the spin-1/2 ${J}_{1}--{J}_{2}$ frustrated Heisenberg antiferromagnet on the square lattice. We have calculated the ground state energy, the magnetic order parameter, the spin stiffness, and several generalized susceptibilities to probe magnetically disordered quantum valence-bond phases. We have found that the quantum critical points for both the N\'eel and collinear orders are ${J}_{2}^{c1}\ensuremath{\approx}(0.44\ifmmode\pm\else\textpm\fi{}0.01){J}_{1}$ and ${J}_{2}^{c2}\ensuremath{\approx}(0.59\ifmmode\pm\else\textpm\fi{}0.01){J}_{1}$, respectively, which are in good agreement with the results obtained by other approximations. In contrast to the recent study by [Sirker et al. Phys. Rev. B 73, 184420 (2006)], our data do not provide evidence for the transition from the N\'eel to the valence-bond solid state to be first order. Moreover, our results are in favor of the deconfinement scenario for that phase transition. We also discuss the nature of the magnetically disordered quantum phase.

arXiv:0806.3825•Physical Review B•Dec 11, 2008•183 citations

Ground-state phase diagram of quantum Heisenberg antiferromagnets on the anisotropic dimerized square lattice

Munehisa Matsumoto, Chitoshi Yasuda, Synge Todo +1 more

The $S=1/2$ and $S=1$ two-dimensional quantum Heisenberg antiferromagnets on the anisotropic dimerized square lattice are investigated by the quantum Monte Carlo method. By finite-size-scaling analyses on the correlation lengths, the ground-state phase diagram parametrized by strengths of the dimerization and of the spatial anisotropy is determined much more accurately than the previous works. It is confirmed that the quantum critical phenomena on the phase boundaries belong to the same universality class as that of the classical three-dimensional Heisenberg model. Furthermore, for $S=1,$ we show that all the spin-gapped phases, such as the Haldane and dimer phases, are adiabatically connected in the extended-parameter space, though they are classified into different classes in terms of the string order parameter in the one-dimensional, i.e., the zero-interchain-coupling, case.

arXiv:cond-mat/0107115•Physical review. B, Condensed matter•Nov 30, 2001•182 citations

Quantum phase transition in a Heisenberg antiferromagnet on a square lattice with strong plaquette interactions

A. Fabricio Albuquerque, Matthias Troyer, J. Oitmaa

We present numerical results for an $S=1/2$ Heisenberg antiferromagnet on an inhomogeneous square lattice with tunable interaction between spins belonging to different plaquettes. Employing quantum Monte Carlo, we significantly improve on previous results for the critical point separating singlet-disordered and N\'eel-ordered phases and obtain an estimate for the critical exponent $\ensuremath{\nu}$ consistent with the three-dimensional classical Heisenberg universality class. Additionally, we show that a fairly accurate result for the critical point can be obtained from a contractor renormalization expansion by applying a surprisingly simple analysis to the effective Hamiltonian.

arXiv:0807.4389•Physical Review B•Oct 3, 2008•32 citations

Spontaneous dimer order, excitation spectrum and quantum-phase transitions in the J 1 - J 2 Heisenberg model

Jaan Oitmaa Valeri N. Kotov

We overview some recent work and present new results on the ground-state properties and the spectrum of excitations of the two-dimensional frustrated Heisenberg antiferromagnet. Spontaneous dimer order is present in the quantum disordered phase of this model. We study the stability and analyse the structure of the spectrum, including the two-particle singlet excitation branch throughout the disordered phase, as well as in the vicinity of the Neel critical point. The variation in the dimer order parameter is also given, and it is argued that near the critical point it reflects the presence of the low-energy singlet bound state.

Philosophical Magazine B•Jul 11, 2000•10 citations

Spontaneous dimer order, excitation spectrum and quantum-phase transitions in the J1-J2 Heisenberg model

Valeri N. Kotov, J. Oitmaa, Oleg P. Sushkov +1 more

We overview some recent work and present new results on the ground-state properties and the spectrum of excitations of the two-dimensional frustrated Heisenberg antiferromagnet. Spontaneous dimer order is present in the quantum disordered phase of this model. We study the stability and analyse the structure of the spectrum, including the two-particle singlet excitation branch throughout the disordered phase, as well as in the vicinity of the Neel critical point. The variation in the dimer order parameter is also given, and it is argued that near the critical point it reflects the presence of the low-energy singlet bound state.

arXiv:cond-mat/9912228•Philosophical Magazine B•Aug 1, 2000•34 citations

Dimerized Phase and Transitions in a Spatially Anisotropic Square Lattice Antiferromagnet

Oleg A. Starykh, Leon Balents

We investigate the spatially anisotropic square lattice quantum antiferromagnet. The model describes isotropic spin-1/2 Heisenberg chains (exchange constant J) coupled antiferromagnetically in the transverse (J( perpendicular )) and diagonal (J(x)), with respect to the chain, directions. Classically, the model admits two ordered ground states-with antiferromagnetic and ferromagnetic interchain spin correlations-separated by a first-order phase transition at J( perpendicular )=2J(x). We show that in the quantum model this transition splits into two, revealing an intermediate quantum-disordered columnar dimer phase, both in two dimensions and in a simpler two-leg ladder version. We describe quantum-critical points separating this spontaneously dimerized phase from classical ones.

arXiv:cond-mat/0402055•Physical Review Letters•Sep 15, 2004•128 citations
We have developed a general scheme for carrying out systematic perturbation expansions for groundstate properties of quantum lattice models. As an application, we study the onset of spontaneous N'eel order in S=12S=\frac{1}{2}S=21​ Heisenberg antiferromagnets by expanding around dimerized Hamiltonians. In one dimension (1D) we recover accurately the known exact results. On the square lattice we find novel critical points separating N'eel ordered and disordered phases; the estimated critical exponents are consistent with those of the 3D classical Heisenberg model.
Using the coupled cluster method for high orders of approximation and complementary exact diagonalization studies we investigate the ground state properties of the spin-1/2 J1−−J2{J}_{1}--{J}_{2}J1​−−J2​ frustrated Heisenberg antiferromagnet on the square lattice. We have calculated the ground state energy, the magnetic order parameter, the spin stiffness, and several generalized susceptibilities to probe magnetically disordered quantum valence-bond phases. We have found that the quantum critical points for both the N\'eel and collinear orders are ${J}_{2}^{c1}\ensuremath{\approx}(0.44\ifmmode\pm\else\textpm\fi{}0.01){J}_{1}$ and ${J}_{2}^{c2}\ensuremath{\approx}(0.59\ifmmode\pm\else\textpm\fi{}0.01){J}_{1}$, respectively, which are in good agreement with the results obtained by other approximations. In contrast to the recent study by [Sirker et al. Phys. Rev. B 73, 184420 (2006)], our data do not provide evidence for the transition from the N\'eel to the valence-bond solid state to be first order. Moreover, our results are in favor of the deconfinement scenario for that phase transition. We also discuss the nature of the magnetically disordered quantum phase.
The S=1/2S=1/2S=1/2 and S=1S=1S=1 two-dimensional quantum Heisenberg antiferromagnets on the anisotropic dimerized square lattice are investigated by the quantum Monte Carlo method. By finite-size-scaling analyses on the correlation lengths, the ground-state phase diagram parametrized by strengths of the dimerization and of the spatial anisotropy is determined much more accurately than the previous works. It is confirmed that the quantum critical phenomena on the phase boundaries belong to the same universality class as that of the classical three-dimensional Heisenberg model. Furthermore, for S=1,S=1,S=1, we show that all the spin-gapped phases, such as the Haldane and dimer phases, are adiabatically connected in the extended-parameter space, though they are classified into different classes in terms of the string order parameter in the one-dimensional, i.e., the zero-interchain-coupling, case.
We present numerical results for an S=1/2S=1/2S=1/2 Heisenberg antiferromagnet on an inhomogeneous square lattice with tunable interaction between spins belonging to different plaquettes. Employing quantum Monte Carlo, we significantly improve on previous results for the critical point separating singlet-disordered and N\'eel-ordered phases and obtain an estimate for the critical exponent $\ensuremath{\nu}$ consistent with the three-dimensional classical Heisenberg universality class. Additionally, we show that a fairly accurate result for the critical point can be obtained from a contractor renormalization expansion by applying a surprisingly simple analysis to the effective Hamiltonian.
We overview some recent work and present new results on the ground-state properties and the spectrum of excitations of the two-dimensional frustrated Heisenberg antiferromagnet. Spontaneous dimer order is present in the quantum disordered phase of this model. We study the stability and analyse the structure of the spectrum, including the two-particle singlet excitation branch throughout the disordered phase, as well as in the vicinity of the Neel critical point. The variation in the dimer order parameter is also given, and it is argued that near the critical point it reflects the presence of the low-energy singlet bound state.
We overview some recent work and present new results on the ground-state properties and the spectrum of excitations of the two-dimensional frustrated Heisenberg antiferromagnet. Spontaneous dimer order is present in the quantum disordered phase of this model. We study the stability and analyse the structure of the spectrum, including the two-particle singlet excitation branch throughout the disordered phase, as well as in the vicinity of the Neel critical point. The variation in the dimer order parameter is also given, and it is argued that near the critical point it reflects the presence of the low-energy singlet bound state.
We investigate the spatially anisotropic square lattice quantum antiferromagnet. The model describes isotropic spin-1/2 Heisenberg chains (exchange constant J) coupled antiferromagnetically in the transverse (J( perpendicular )) and diagonal (J(x)), with respect to the chain, directions. Classically, the model admits two ordered ground states-with antiferromagnetic and ferromagnetic interchain spin correlations-separated by a first-order phase transition at J( perpendicular )=2J(x). We show that in the quantum model this transition splits into two, revealing an intermediate quantum-disordered columnar dimer phase, both in two dimensions and in a simpler two-leg ladder version. We describe quantum-critical points separating this spontaneously dimerized phase from classical ones.