Quantum spin chains with multiple dynamics

Abstract

Many-body systems with multiple emergent time scales arise in various contexts, including classical critical systems, correlated quantum materials, and ultra-cold atoms. We investigate such non-trivial quantum dynamics in a new setting: a spin-1 bilinear-biquadratic chain. It has a solvable entangled groundstate, but a gapless excitation spectrum that is poorly understood. By using large-scale DMRG simulations, we find that the lowest excitations have a dynamical exponent $z$ that varies from 2 to 3.2 as we vary a coupling in the Hamiltonian. We find an additional gapless mode with a continuously varying exponent $2\le z<2.7$, which establishes the presence of multiple dynamics. In order to explain these striking properties, we construct a continuum wavefunction for the groundstate, which correctly describes the correlations and entanglement properties. We also give a continuum parent Hamiltonian, but show that additional ingredients are needed to capture the excitations of the chain. By using an exact mapping to the non-equilibrium dynamics of a classical spin chain, we find that the large dynamical exponent is due to subdiffusive spin motion. Finally, we discuss the connections to other spin chains and to a family of quantum critical models in 2d.

4+5 pages, 2+4 figures, 1 table. v2: minor changes to reflect the published version

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• Logarithmic Negativity in Quantum Lifshitz Theories
• Relating bulk to boundary entanglement
• Lifshitz entanglement entropy from holographic cMERA
• Slow dynamics and large deviations in classical stochastic Fredkin chains
• A Field Theory Study of Entanglement Wedge Cross Section: Odd Entropy
• Entanglement susceptibilities and universal geometric entanglement entropy
• The Fredkin staircase: An integrable system with a finite-frequency Drude peak
• The pair-flip model: a very entangled translationally invariant spin chain
• Slow dynamics of the Fredkin spin chain
• Coupled Fredkin and Motzkin chains from quantum six- and nineteen-vertex models
• Deforming the Fredkin spin chain away from its frustration-free point
• Subdiffusive transport in the Fredkin dynamical universality class
• Entanglement after Quantum Quenches in Lifshitz Scalar Theories
• Dynamics and correlations in Motzkin and Fredkin spin chains
• Entanglement in Lifshitz Fermion Theories
• Quantum lozenge tiling and entanglement phase transition
• Tunable quantum spin chain with three-body interactions