Fate of the one-dimensional Ising quantum critical point coupled to a gapless boson

Abstract

The problem of a quantum Ising degree of freedom coupled to a gapless bosonic mode appears naturally in many one dimensional systems, yet surprisingly little is known how such a coupling affects the Ising quantum critical point. We investigate the fate of the critical point in a regime, where the weak coupling renormalization group (RG) indicates a flow toward strong coupling. Using a renormalization group analysis and numerical density matrix renormalization group (DMRG) calculations we show that, depending on the ratio of velocities of the gapless bosonic mode and the Ising critical fluctuations, the transition may remain continuous or become fluctuation-driven first order. The two regimes are separated by a tri-critical point of a novel type.

arXiv comment8 pages, 8 figures; published version

References in corpus (16)

• Bosonization and Strongly Correlated Systems
• Structural phase transitions in low-dimensional ion crystals
• Quantum zigzag transition in ion chains
• Topological States in a One-Dimensional Fermi Gas with Attractive Interactions
• Transition from a one-dimensional to a quasi-one-dimensional state in interacting quantum wires
• Emergent Lorentz symmetry with vanishing velocity in a critical two-subband quantum wire
• Zigzag Phase Transition in Quantum Wires
• Emergent supersymmetry at the Ising-Berezinskii-Kosterlitz-Thouless multicritical point
• Non-local Order in Elongated Dipolar Gases
• A supersymmetric multicritical point in a model of lattice fermions
• Vortices in coupled planes with columnar disorder and bosonic ladders
• Exotic Quantum Criticality in One-Dimensional Coupled Dipolar Bosons Tubes
• Collective Edge Modes near the onset of a graphene quantum spin Hall state
• From classical to quantum criticality
• Ion-trap simulation of the quantum phase transition in an exactly solvable model of spins coupled to bosons
• Topological quasi-one-dimensional state of interacting spinless electrons

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• Quantum field theory of nematic transitions in spin orbit coupled spin-1 polar bosons
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• Strongly interacting spin-orbit coupled Bose-Einstein condensates in one dimension
• Lattice vibration as a knob for novel quantum criticality: Emergence of supersymmetry from spin-lattice coupling
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• Quantum Phases of a Weakly Disordered Josephson Ladder
• Spin-orbit coupled bosons in one dimension: emergent gauge field and Lifshitz transition
• Quantum critical behaviors and decoherence of weakly coupled quantum Ising models within an isolated global system
• Stacked quantum Ising systems and quantum Ashkin-Teller model
• Melting of three-sublattice order in triangular lattice Ising antiferromagnets: Power-law order, $Z_6$ parafermionic multicriticality, and weakly first order transitions