Physical Review Letters

Spontaneous symmetry breaking in quantum frustrated antiferromagnets

P. Azaria, Bertrand Delamotte, D. Mouhanna

Published Apr 19, 1993• 64 citations

Abstract

We show that the spontaneous symmetry breaking mechanism in quantum antiferromagnets is due to the collapse, in the thermodynamical limit, of an infinite set of excited states onto the ground state. We characterize both the nature and the scaling of the relevant tower of states for the quantum antiferromagnet on the triangular lattice. Comparison with recent numerical results for the S=1/2 case gives strong support for the existence of long range order in this system.

DOI: 10.1103/physrevlett.70.2483

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Physical Review Letters

Spontaneous symmetry breaking in quantum frustrated antiferromagnets

P. Azaria, Bertrand Delamotte, D. Mouhanna

Published Apr 19, 1993• 64 citations

Publisher

Abstract

DOI: 10.1103/physrevlett.70.2483

Related papers

Symmetry Breaking and Finite Size Effects in Quantum Many-Body Systems 1

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Songtai Lv, Yuchen Meng, Haiyuan Zou

Frustration on the triangular lattice has long been a source of intriguing and often debated phases in many-body systems. Although symmetry analysis has been employed, the role of the seemingly trivial parity symmetry has received little attention. In the work described in this Letter, we show that phases induced by frustration are systematically shaped by an implicit rule of thumb associated with spontaneous parity breaking in weak longitudinal field. This principle enables us to anticipate and rationalize the regimes and conditions under which nontrivial phases emerge. For the spin- $S$ antiferromagnetic XXZ model, we demonstrate that a controversial parity-broken phase appears at intermediate values of $S$ . In bilayer systems, enhanced frustration leads to additional phases, such as supersolids, whose properties can be classified by their characteristic parity features. Benefiting from our improved tensor network contraction techniques, we confirm these results through large-scale tensor-network calculations. This study offers an alternative viewpoint and a systematic approach for examining the interplay between spin, symmetry, and frustration in many-body systems.Frustration on the triangular lattice has long been a source of intriguing and often debated phases in many-body systems. Although symmetry analysis has been employed, the role of the seemingly trivial parity symmetry has received little attention. In the work described in this Letter, we show that phases induced by frustration are systematically shaped by an implicit rule of thumb associated with spontaneous parity breaking in weak longitudinal field. This principle enables us to anticipate and rationalize the regimes and conditions under which nontrivial phases emerge. For the spin-$S$ antiferromagnetic XXZ model, we demonstrate that a controversial parity-broken phase appears at intermediate values of $S$. In bilayer systems, enhanced frustration leads to additional phases, such as supersolids, whose properties can be classified by their characteristic parity features. Benefiting from our improved tensor network contraction techniques, we confirm these results through large-scale tensor-network calculations. This study offers an alternative viewpoint and a systematic approach for examining the interplay between spin, symmetry, and frustration in many-body systems.

cond-mat.str-elCross-listedarXiv:2602.05901Physical Review LettersFeb 6, 20260 citations

We calculate the order parameter m in the infinite-range isotropic-interaction quantum model of antiferromagnetism due to Lieb and Mattis (LM). The Hamiltonian

{\mathit{H}}_{1}

in this model contains pure Heisenberg interactions. m is the mean value of the z component

{\mathit{m}}_{\mathit{s}}^{\mathit{z}}

of the staggered spin per particle

{\mathbf{m}}_{\mathit{s}}

in the ground state of

{\mathit{H}}_{1}

plus a symmetry-breaking term

{\mathit{H}}_{\mathit{B}}

due to an infinitesimal staggered field B in the thermodynamic limit (TL). We find a value of \ensuremath{\surd}3 for the ratio r=m/

{\mathit{m}}_{0}

{\mathit{m}}_{0}

being the root-mean-square value of

{\mathit{m}}_{\mathit{s}}^{\mathit{z}}

for B==0 in the TL. m and

{\mathit{m}}_{0}

measure, respectively, the spontaneous symmetry breaking and the amount of long-range order in the symmetry-unbroken state. This value is expected on the basis of our recent argument that r= \ensuremath{\surd}3 if

{\mathbf{m}}_{\mathit{s}}

behaves in the TL as a classical vector with no magnitude fluctuations---behavior that we show holds for the Lieb-Mattis model. The addition to

{\mathit{H}}_{1}

of a small easy-axis anisotropic term is also discussed briefly. These studies allow calculation of the size dependence of quantities that we have recently shown to become lower bounds on m in the TL (bounds that are valid for short-range-interaction models as well). In the LM model, low-lying energy eigenstates with excitation energies of order ${\mathit{N}}^{\mathrm{\ensuremath{-}}1}$, where N is the number of spins, form a continuum (with no gap) in the TL. These are closely related to similar states shown to exist for the nearest-neighbor isotropic Heisenberg antiferromagnet. We show that this continuum has a density of states that is O(

{\mathit{N}}^{0}

); i.e., it is not extensive.

S

antiferromagnetic XXZ model, we demonstrate that a controversial parity-broken phase appears at intermediate values of

S

. In bilayer systems, enhanced frustration leads to additional phases, such as supersolids, whose properties can be classified by their characteristic parity features. Benefiting from our improved tensor network contraction techniques, we confirm these results through large-scale tensor-network calculations. This study offers an alternative viewpoint and a systematic approach for examining the interplay between spin, symmetry, and frustration in many-body systems.