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arXiv:2306.00690 · Physical review. B./Physical review. B

Quantum many-body scars in spin-1 Kitaev chain with uniaxial single-ion anisotropy

Wen-Yi Zhang, Yanan Wang, Dongchang Liu, Jie Ren, Jia Li, Ning Wu, Andrzej M. Oleś, Wen‐Long You

Published Sep 13, 2023• 10 citations
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Abstract

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 ${\mathbb{Z}}_{2}$ 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 ${D}_{c}$, 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 $D<{D}_{c}$. Finally, we investigate the evolution of phase boundaries of the Kitaev spin liquid and dimer phase by introducing Heisenberg interactions, which spoil the ${\mathbb{Z}}_{2}$ 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.

DOI
10.1103/physrevb.108.104411

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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.
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 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 $\ensuremath{\theta}$ 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.
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.
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.
Experimental observation of coherent oscillations in a Rydberg atom chain [H. Bernien et al., Nature (London) 551, 579 (2017)] has led to the discovery of quantum many-body scars (QMBSs) which is a new paradigm for ergodicity breaking. The experimental findings in the Rydberg chain can be well captured by a kinetically constrained model called the ``PXP'' model, which has been shown to host the eigenstate thermalization hypothesis (ETH)-violating scar states in the middle of the spectrum. Much effort has been put into identifying similar kinetically restricted systems that show a violation of ETH. In this paper, we study the QMBSs that can arise in one such model, namely the spin-1 Kitaev chain, where owing to some conserved quantities, the Hilbert space gets fragmented into unequal disconnected subspaces. Recently, You et al. [Phys. Rev. Res. 4, 013103 (2022)] showed that the ground state sector of this chain can be mapped exactly onto the prototypical PXP model and thus hosts QMBSs. Here, we demonstrate that the phenomenon of scarring is also present in other sectors, and in particular, we identify a sector that exhibits substantially more scarring than the ground state one. We propose an initial state and numerically demonstrate that its fidelity revivals are pronounced and longer lived than those in the PXP model.
We investigate the ground-state phase diagram for a spin-one quantum Heisenberg antiferromagnetic chain with exchange and single-ion anisotropies in an external magnetic field by using the infinite time-evolving block decimation algorithm to compute the ground-state fidelity per lattice site. We detect all phase boundaries solely by computing the ground-state fidelity per lattice site, with the prescription that a phase transition point is attributed to a pinch point on the ground-state fidelity surface. Furthermore, the results indicate that a magnetization plateau corresponds to a fidelity plateau on the ground-state fidelity surface, thus offering an alternative route for investigating the magnetization processes of quantum many-body spin systems. We characterize all phases by using the local-order parameter, the spin correlation, the momentum distribution of the spin correlation structure factor, and mutual information as a function of the lattice distance. The commensurate and incommensurate phases are distinguished by the mutual information. In addition, the central charges at criticalities are identified by performing a finite-entanglement scaling analysis. The results show that all phase transitions between spin liquids and magnetization plateaus belong to the Pokrovsky-Talapov universality class.
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.