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arXiv:2209.07824 · Physical review. B./Physical review. B

Hybrid symmetry breaking in classical spin models with subsystem symmetries

Giovanni Canossa, Lode Pollet, Ke Liu

Published Feb 22, 2023• 2 citations
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Abstract

We investigate two concrete cases of phase transitions breaking a subsystem symmetry. The models are two classical compass models featuring line-flip and plane-flip symmetries and correspond to special limits of a Heisenberg-Kitaev Hamiltonian on a cubic lattice. We show that these models experience a hybrid symmetry breaking by which the system display distinct symmetry broken patterns in different submanifolds. For instance, the system may look magnetic within a chain or plane but nematic-like when observing from one dimensionality higher. We fully characterize the symmetry-broken phases by a set of subdimensional order parameters and confirm numerically both cases undergo a non-standard first-order phase transition. Our results provide new insights into phase transitions involving subsystem symmetries and generalize the notion of conventional spontaneous symmetry breaking.

DOI
10.1103/physrevb.107.054431

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We investigate two concrete cases of phase transitions breaking a subsystem symmetry. The models are two classical compass models featuring line-flip and plane-flip symmetries and correspond to special limits of a Heisenberg-Kitaev Hamiltonian on a cubic lattice. We show that these models experience a hybrid symmetry breaking by which the system display distinct symmetry broken patterns in different submanifolds. For instance, the system may look magnetic within a chain or plane but nematic-like when observing from one dimensionality higher. We fully characterize the symmetry-broken phases by a set of subdimensional order parameters and confirm numerically both cases undergo a non-standard first-order phase transition. Our results provide new insights into phase transitions involving subsystem symmetries and generalize the notion of conventional spontaneous symmetry breaking.
We determine the finite-temperature phase diagram and critical behavior of the classical square-lattice Heisenberg-compass model using large-scale Monte Carlo simulations and finite-size scaling. Six symmetry distinct ordered phases are identified. The four phases that simultaneously break the spin-lattice C4C_4C4​ and in-plane spin-inversion symmetries undergo continuous transitions in the Ashkin-Teller universality class, with the associated critical lines terminating at four-state Potts points, beyond which the transitions become first order. In contrast, the two zzz-polarized phases display conventional two-dimensional Ising criticality. Our results reveal how the interplay between Heisenberg exchange and compass anisotropy organizes these distinct critical regimes, thereby completing the characterization of the model's thermal phase transitions.
The spontaneous breaking of noninvertible symmetries can lead to exotic phenomena such as the coexistence of order and disorder. Here, we explore second-order phase transitions in one-dimensional spin chains between two phases that correspond to distinct patterns of noninvertible symmetry breaking. The critical point shares several features with well-understood examples of deconfined quantum critical points, such as enlarged symmetry and identical exponents for the two order parameters participating in the transition. Interestingly, such deconfined transitions involving noninvertible symmetries allow one to construct a whole family of similar critical points by gauging spin-flip symmetries. By employing gauging and bosonization, we characterize the phase diagram of our model in the vicinity of the critical point. We also explore proximate phases and phase transitions in related models, including a deconfined quantum critical point between invertible order parameters that is enforced by a noninvertible symmetry.
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The higher-spin Kitaev magnets, in which the Kitaev interaction and off-diagonal exchange couplings are overwhelmingly large, have emerged as a fertile avenue to explore exotic phases and unusual excitations. In this paper, we study the quantum phase diagram of the spin-1 Kitaev-$\mathrm{\ensuremath{\Gamma}}$ model on the honeycomb lattice using density-matrix renormalization group. It harbors six distinct phases and the intriguing findings are three magnetically ordered phases in which both time-reversal symmetry and lattice symmetry, albeit of different sorts, are broken spontaneously. The chiral spin state originates from the order-by-disorder effect and exhibits an almost saturated scalar spin chirality at the quantum level. Depending on the relative strength of the two interactions, it also features a columnarlike or plaquettelike dimer pattern as a consequence of the translational symmetry breaking. In parallel, the nematic ferromagnets are situated at the ferromagnetic Kitaev side and possess small but finite ferromagnetic ordering. The lattice-rotational symmetry breaking enforces nonequivalent bond energy along one of the three bonds. Although the intrinsic difference between the two nematic ferromagnets remains elusive, the discontinuities in the von Neumann entropy, hexagonal plaquette operator, and Wilson loop operator convincingly suggest that they are separated via a first-order phase transition.
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A minimal Kitaev-Gamma model has been recently investigated to understand various Kitaev systems. In the one-dimensional Kitaev-Gamma chain, an emergent SU(2)1\mathrm{SU}{(2)}_{1}SU(2)1​ phase and a rank-1 spin ordered phase with ${O}_{h}\ensuremath{\rightarrow}{D}_{4}$ symmetry breaking were identified using non-Abelian bosonization and numerical techniques. However, puzzles near the antiferromagnetic Kitaev region with finite Gamma interaction remained unresolved. Here we focus on this parameter region and find that there are two new phases, namely, a rank-1 ordered phase with an ${O}_{h}\ensuremath{\rightarrow}{D}_{3}$ symmetry breaking, and a peculiar Kitaev phase. Remarkably, the ${O}_{h}\ensuremath{\rightarrow}{D}_{3}$ symmetry breaking corresponds to the classical magnetic order, but appears in a region very close to the antiferromagnetic Kitaev point where the quantum fluctuations are presumably very strong. In addition, a two-step symmetry breaking ${O}_{h}\ensuremath{\rightarrow}{D}_{3d}\ensuremath{\rightarrow}{D}_{3}$ is numerically observed as the length scale is increased: At short and intermediate length scales, the system behaves as having a rank-2 spin nematic order with ${O}_{h}\ensuremath{\rightarrow}{D}_{3d}$ symmetry breaking; and at long distances, time reversal symmetry is further broken leading to the ${O}_{h}\ensuremath{\rightarrow}{D}_{3}$ symmetry breaking. Finally, there is no numerical signature of spin orderings nor Luttinger liquid behaviors in the Kitaev phase whose nature is worth further studies.