Highly-symmetric random one-dimensional spin models

Abstract

The interplay of disorder and interactions is a challenging topic of condensed matter physics, where correlations are crucial and exotic phases develop. In one spatial dimension, a particularly successful method to analyze such problems is the strong-disorder renormalization group (SDRG). This method, which is asymptotically exact in the limit of large disorder, has been successfully employed in the study of several phases of random magnetic chains. Here we develop an SDRG scheme capable to provide in-depth information on a large class of strongly disordered one-dimensional magnetic chains with a global invariance under a generic continuous group. Our methodology can be applied to any Lie-algebra valued spin Hamiltonian, in any representation. As examples, we focus on the physically relevant cases of SO(N) and Sp(N) magnetism, showing the existence of different randomness-dominated phases. These phases display emergent SU(N) symmetry at low energies and fall in two distinct classes, with meson-like or baryon-like characteristics. Our methodology is here explained in detail and helps to shed light on a general mechanism for symmetry emergence in disordered systems.

26 pages, 12 figures

References in corpus (12)

• "Deconfined" quantum critical points
• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Class of exactly solvable SO(n) symmetric spin chains with matrix product ground states
• Strong Disorder RG approach - a short review of recent developments
• Effects of dissipation on a quantum critical point with disorder
• Increasing of entanglement entropy from pure to random quantum critical chains
• Low-energy properties of aperiodic quantum spin chains
• Emergent Symmetry and Dimensional Reduction at a Quantum Critical Point
• Phase diagrams and universality classes of random antiferromagnetic spin ladders
• Rounding of a first-order quantum phase transition to a strong-coupling critical point
• Random Antiferromagnetic SU(N) Spin Chains
• Adaptive Density Matrix Renormalization Group for Disordered Systems

Cited by in corpus (8)

• Strong Disorder RG approach - a short review of recent developments
• Aperiodic spin chains at the boundary of hyperbolic tilings
• The correlation functions of certain random antiferromagnetic spin-1/2 critical chains
• Adaptive Density-Matrix Renormalization-Group study of the disordered antiferromagnetic spin-1/2 Heisenberg chain
• Random free-fermion quantum spin chain with multi-spin interactions
• The case of SU$(3)$ criticality in spin-2 chains
• Emergent SU(N) symmetry in disordered SO(N) spin chains
• Signatures of infinite randomness in transport properties of disordered spin chains