One-dimensional model for deconfined criticality with Z3×Z3 symmetry

Abstract

We continue recent efforts to discover examples of deconfined quantum criticality in one-dimensional models. In this work we investigate the transition between a Z 3 ferromagnet and a phase with valence bond solid (VBS) order in a spin chain with Z 3 × Z 3 global symmetry. We study a model with alternating projective representations on the sites of the two sublattices, allowing the Hamiltonian to connect to an exactly solvable point having VBS order with the character of SU(3)-invariant singlets. Such a model does not admit a Lieb-Schultz-Mattis theorem typical of systems realizing deconfined critical points. Nevertheless, we find evidence for a direct transition from the VBS phase to a Z 3 ferromagnet. Finite-entanglement scaling data are consistent with a second-order or weakly first-order transition. We find in our parameter space an integrable lattice model apparently describing the phase transition, with a very long, finite, correlation length of 190878 lattice spacings. Based on exact results for this model, we propose that the transition is extremely weakly first order and is part of a family of deconfined quantum critical points described by walking of renormalization group flows.

Continuous phase transition from a chiral spin state to collinear magnetic order in a zigzag chain with Kitaev interactions

“…Furthermore, a low-energy parton construction suggests an emergent symmetry along with the condensation of topological defects (domain walls) in the transition, similar to the phenomenology found in deconfined quantum criticality in two dimensions. Our work then provides an example of the recently found deconfined transitions in one dimension [30,31,34].…”

“…Unambiguous numerical demonstrations of DQC in lattice models [25,26] have been hindered by logarithmic corrections to finite-size scaling, which make it difficult to rule out a weakly first-order transition [27][28][29]. This challenge has motivated the study of Landau-forbidden transitions with analogies to DQC in one-dimensional (1D) models [30][31][32][33][34], for which more controllable analytical and numerical methods are available. In fact, it has been known for a while that the same operator that gives rise to Néel order in the field theory for anisotropic spin-1/2 chains can also generate spontaneous dimerization [35].…”

Dynamical signatures of the one-dimensional deconfined quantum critical point

“…Recently, some works studied possible DQCP in one-dimensional (1D) spin systems and obtained some interesting results. [20][21][22][23][24][25][26][27][28][29][30][31][32] An advantage of the 1D quantum spin systems over their 2D counterparts is that many powerful and well controlled analytical and numerical techniques, such as Bethe-ansatz, bosonization, and density matrix renormalization group (DMRG) [33][34][35] can be applied, and hence the results are more convincing. Meanwhile, enhanced quantum fluctuations in 1D employ strong constraint to ground-state properties, as involved in the Lieb-Schultz-Mattis (LSM) theorem.…”

Dynamical signatures of the one-dimensional deconfined quantum critical point

“…To realize a DQCP in realistic 2D spin models or even in experimental quantum magnets [19] is, however, still a challenging task. Recently, some works studied possible DQCP in onedimensional (1D) spin systems and obtained some interesting results [20][21][22][23][24][25][26][27][28][29][30][31][32]. An advantage of the 1D quantum spin systems over their 2D counterparts is that many powerful and well controlled analytical and numerical techniques, such as Bethe-ansatz, bosonization, and density matrix renormalization group (DMRG) [33][34][35] can be applied, and hence the results are more convincing.…”