Abstract

We study the phases and phase transitions of a disordered one-dimensional quantum q-state clock Hamiltonian using large-scale Monte Carlo simulations. Making contact with earlier results, we confirm that the clean, translational invariant version of the model, for q=6, hosts an intermediate emergent quasi-long-range ordered (QLRO) phase between the symmetry-broken true long-range ordered (TLRO) phase and the disordered (paramagnetic) phase. With increasing disorder strength, the quasi-long-range ordered phase shrinks and finally vanishes at a multicritical point, beyond which there is a direct transition from the TLRO phase to the paramagnetic phase. After establishing the phase diagram, we characterize the critical behaviors of the various quantum phase transitions in the model. We find that weak disorder is an irrelevant perturbation of the Berezinskii-Kosterlitz-Thouless transitions that separate the QLRO phase from the TLRO and paramagnetic phases. For stronger disorder, some of the critical exponents become disorder-dependent already before the system reaches the multicritical point. We also show that beyond the multicritical point, the direct transition from the TLRO phase to the paramagnetic phase is governed by an infinite-randomness critical point in line with strong-disorder renormalization group predictions. While our numerical results are for q=6, we expect the qualitative features of the behavior to hold for all q>4.

Department(s)

Physics

Comments

Institute of International Education, Grant DST/ICPS/QuST/Theme-3/2019/Q69

International Standard Serial Number (ISSN)

2469-9969; 2469-9950

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 2025 American Physical Society, All rights reserved.

Publication Date

01 Mar 2025

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