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arXiv:2405.13281 · Physical review. B./Physical review. B

Exploring quantum criticality and ergodicity-breaking dynamics in spin-1 Kitaev chains via single-ion anisotropies

Wen-Yi Zhang, Qingmin Hu, Jie Ren, Liangsheng Li, Wen‐Long You

Published Oct 25, 2024• 4 citations
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Abstract

We investigate topological gauge-theory terms and quantum criticality in a spin-1 Kitaev chain with general single-ion anisotropies (SIAs). The ground-state phase diagram, including the Kitaev spin liquid (KSL) and gapless dimer phases, is determined by the infinite time evolving block decimation (iTEBD) method. A quantum phase transition between the KSL and dimer phases occurs by varying uniaxial SIA, analogous to the confinement-deconfinement transition in the lattice Schwinger model with a topological $\ensuremath{\theta}$ angle of $\ensuremath{\pi}$. Introducing rhombic SIA shifts this angle from $\ensuremath{\pi}$, resulting in $y$- and $x$-ferroquadrupole phases. The transition between these phases can occur through a crossover in the KSL phase or a genuine phase transition along a deconfined line. We map the spin-1 Hamiltonian to an effective spin-1/2 PXP Hamiltonian, with uniaxial SIA corresponding to uniform detuning and rhombic SIA to staggered detuning. We explore the hierarchical fragmentation of the Hilbert space, revealing that quantum many-body scars (QMBSs) emerge under weak uniform detuning, while slow dynamics under large staggered detuning is accurately captured by a second-order effective Hamiltonian via the Schrieffer-Wolff transformation. Our work establishes a framework for simulating topological $\ensuremath{\theta}$ angles and ergodicity-breaking dynamics, bridging higher-spin generalizations of scarred models with lattice gauge theories, potentially realizable using state-of-the-art cold-atom quantum simulators.

DOI
10.1103/physrevb.110.134441

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We investigate topological gauge-theory terms and quantum criticality in a spin-1 Kitaev chain with general single-ion anisotropies (SIAs). The ground-state phase diagram, including the Kitaev spin liquid (KSL) and gapless dimer phases, is determined by the infinite time evolving block decimation (iTEBD) method. A quantum phase transition between the KSL and dimer phases occurs by varying uniaxial SIA, analogous to the confinement-deconfinement transition in the lattice Schwinger model with a topological \ensuremathθ\ensuremath{\theta}\ensuremathθ angle of \ensuremathπ\ensuremath{\pi}\ensuremathπ. Introducing rhombic SIA shifts this angle from \ensuremathπ\ensuremath{\pi}\ensuremathπ, resulting in yyy- and xxx-ferroquadrupole phases. The transition between these phases can occur through a crossover in the KSL phase or a genuine phase transition along a deconfined line. We map the spin-1 Hamiltonian to an effective spin-1/2 PXP Hamiltonian, with uniaxial SIA corresponding to uniform detuning and rhombic SIA to staggered detuning. We explore the hierarchical fragmentation of the Hilbert space, revealing that quantum many-body scars (QMBSs) emerge under weak uniform detuning, while slow dynamics under large staggered detuning is accurately captured by a second-order effective Hamiltonian via the Schrieffer-Wolff transformation. Our work establishes a framework for simulating topological \ensuremathθ\ensuremath{\theta}\ensuremathθ angles and ergodicity-breaking dynamics, bridging higher-spin generalizations of scarred models with lattice gauge theories, potentially realizable using state-of-the-art cold-atom quantum simulators.
To establish a solid-state-based framework for the coexistence of quantum many-body scars and quantum criticality, we investigate the spin-1 Kitaev chain with uniaxial single-ion anisotropy (SIA). In the subspace with uniform Z2{\mathbb{Z}}_{2}Z2​ gauge fields, this model can be exactly mapped to the spin-1/2 effective detuned PXP Hamiltonian, where the SIA plays a role of the static detuning term. The quench dynamics starting from the product states is symmetric between positive and negative values of the SIA, while a quantum phase transition from the Kitaev spin liquid to the dimer phase only occurs at the critical point with a negative Dc{D}_{c}Dc​, implying the spontaneous breaking of the translational symmetry. We find that the coherent oscillations of quantum fidelity and certain local observables are sustained against small SIA perturbations in a quantum quench from special initial states. While the oscillation amplitudes of these observables decay with time as the SIA strength is increased, the system completely thermalizes upon approaching the critical point. In contrast, the initial polarized state, which shows an absence of revivals of quantum fidelity, will exhibit long revivals for D<DcD<{D}_{c}D<Dc​. Finally, we investigate the evolution of phase boundaries of the Kitaev spin liquid and dimer phase by introducing Heisenberg interactions, which spoil the Z2{\mathbb{Z}}_{2}Z2​ gauge fields. A complete phase diagram is given by the infinite time-evolving block decimation method and the ground-state properties of each phase are accurately captured by various spin correlations. Our paper opens the door to understanding exotic connections between many-body scars and quantum criticality in systems with higher spins.
Kitaev-type spin chains have been demonstrated to be fertile playgrounds in which exotic phases and unconventional phase transitions are ready to appear. In this work, we use the density-matrix renormalization-group method to study the quantum phase diagram of a spin-1 Kitaev chain with a tunable negative single-ion anisotropy (SIA). When the strength of the SIA is small, the ground state is revealed to be a spin-nematic phase, which escapes conventional magnetic order but is characterized by a finite spin-nematic correlation because of the breaking spin-rotational symmetry. As the SIA increases, the spin-nematic phase is taken over by either a dimerized phase or an antiferromagnetic phase through an Ising-type phase transition, depending on the direction of the easy axis. For large enough SIA, the dimerized phase and the antiferromagnetic phase undergo a ``Landau-forbidden'' continuous phase transition, suggesting new platform of deconfined quantum critical point in spin-1 Kitaev chain.
The quantum simulation of gauge theories on synthetic quantum matter devices has gained a lot of traction in the last decade, making possible the observation of a range of exotic quantum many-body phenomena. In this work, we consider the spin- 1 / 2 quantum link formulation of 1 + 1 D quantum electrodynamics with a topological θ -angle, which can be used to tune a confinement-deconfinement transition. Exactly mapping this system onto a PXP model with mass and staggered magnetization terms, we show an intriguing interplay between confinement and the ergodicity-breaking paradigms of quantum many-body scarring and Hilbert-space fragmentation. We map out the rich dynamical phase diagram of this model, finding an ergodic phase at small values of the mass μ and confining potential χ , an emergent integrable phase for large μ , and a fragmented phase for large values of both parameters. We also show that the latter hosts resonances that lead to a vast array of effective models. We propose experimental probes of our findings, which can be directly accessed in current cold-atom setups.
To provide a physical example of quantum scars, we study the many-body scars in the spin-1 Kitaev chain where the so-called PXP Hamiltonian is exactly embedded in the spectra. Regarding the conserved quantities, the Hilbert space is fragmented into disconnected subspaces and we explore the associated constrained dynamics. The continuous revivals of the fidelity and the entanglement entropy when the initial state is prepared in $|{\mathbb{Z}}_{k}\ensuremath{\rangle}$ (k=2,3k=2,3k=2,3) state illustrate the essential physics of the PXP model. We study the quantum phase transitions in the one-dimensional spin-1 Kitaev-Heisenberg model using the density-matrix renormalization group and Lanczos exact diagonalization methods, and determine the phase diagram. We parametrize the two terms in the Hamiltonian by the angle $\ensuremath{\phi}$, where the Kitaev term is $K\ensuremath{\equiv}sin(\ensuremath{\phi})$ and competes with the Heisenberg $J\ensuremath{\equiv}cos(\ensuremath{\phi})$ term. One finds a rich ground-state phase diagram as a function of the angle $\ensuremath{\phi}$. Depending on the ratio $K/J\ensuremath{\equiv}tan(\ensuremath{\phi})$, the system either breaks the symmetry to one of distinct symmetry broken phases, or preserves the symmetry in a quantum spin-liquid phase with frustrated interactions. We find that the scarred state is stable for perturbations which obey Z2{\mathbb{Z}}_{2}Z2​-symmetry, while it becomes unstable against Heisenberg-type perturbations.
Crossover and Changeover in Spin-1 Kitaev-ΓΓΓ Chain with Uniaxial Single-ion Anisotropy
Recent advances in bond-directional spin chains have revealed extensive emergent phenomena and unconventional criticality. Here we investigate the spin-1 Kitaev-ΓΓΓ chain with uniaxial single-ion anisotropy (SIA) using large-scale density-matrix renormalization group calculations and bosonization analysis. Tuning the SIA strength reveals a crossover from the Kitaev phase to the large-DDD phase, evidenced by the excitation gap changing from quadratic to linear, the coexistence and smooth evolution of spin-nematic and string order parameters, and the suppression of the double-peak specific heat. For negative SIA, we uncover a changeover from a first-order transition to a continuous one between the dimerized and Haldane phases. The continuous transition belongs to the \textrm{SU(2)2_22​} Wess-Zumino-Witten universality class with central charge c=3/2c=3/2c=3/2, a rare instance in a system without continuous symmetry. Our results establish the Kitaev-ΓΓΓ chain as a minimal platform for controlling crossover and changeover phenomena.
We investigate the fate of the Kitaev spin liquid (KSL) under the influence of an external magnetic field h in the [001] direction and upon tuning bond anisotropy of the Kitaev coupling Kz keeping Kx=Ky=K . Guided by density matrix renormalization group, exact diagonalization, and with insights from parton mean-field theory, we uncover a field-induced gapless-to-gapless Lifshitz transition from the nodal KSL to an intermediate gapless phase. The intermediate phase sandwiched between hc1 and hc2 , which persists for a wide range of anisotropy Kz/K>0 , is composed of weakly coupled one-dimensional quantum critical chains. This intermediate phase is a dimensional crossover, which asymptotically leads to the one-dimensional quantum Ising criticality characterized by the (1+1)D conformal field theory as the field reaches the phase transition at hc2 . Beyond hc2 the system enters a partially polarized phase describable as effectively decoupled bosonic chains in which spin waves propagate along the one-dimensional zigzag direction. Our findings provide a comprehensive phase diagram and offer insights into the unusual physics of dimensional reduction generated by a uniform magnetic field in an otherwise two-dimensional quantum spin liquid. Published by the American Physical Society 2024