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arXiv:2007.02878 · Physical review. B./Physical review. B

Quantum phase transitions in a spin-1 antiferromagnetic chain with long-range interactions and modulated single-ion anisotropy

Jie Ren, Wen‐Long You, Andrzej M. Oleś

Published Jul 17, 2020• 21 citations
arXivHTMLPDF

Abstract

We study the phase diagram of a spin-1 antiferromagnetic chain with isotropic antiferromagnetic interactions decaying with a power law $\ensuremath{\propto}{r}^{\ensuremath{-}\ensuremath{\alpha}}$ $(\ensuremath{\alpha}\ensuremath{\ge}1)$ accompanied by modulated single-ion anisotropy. Employing the techniques of the density-matrix renormalization group, the effects of long-range interactions and single-ion anisotropy on a variety of correlations are investigated. In order to check the consistency, the fidelity susceptibilities are evaluated across quantum phase transitions. The quantum critical points are faithfully detected and orders of phase transitions are determined. The correlation-length critical exponent is extracted from scaling functions of the fidelity susceptibility. The presence of long-range interactions leads to a quantitative change of the phase boundaries and reduces the order of the phase transition under certain conditions. A direct first-order transition between the periodic N\'eel phase and the large-$D$ phase occurs for slowly decaying antiferromagnetic interactions.

DOI
10.1103/physrevb.102.024425

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We study the phase diagram of a spin-1 antiferromagnetic chain with isotropic antiferromagnetic interactions decaying with a power law \ensuremath∝r\ensuremath−\ensuremathα\ensuremath{\propto}{r}^{\ensuremath{-}\ensuremath{\alpha}}\ensuremath∝r\ensuremath−\ensuremathα (\ensuremathα\ensuremath≥1)(\ensuremath{\alpha}\ensuremath{\ge}1)(\ensuremathα\ensuremath≥1) accompanied by modulated single-ion anisotropy. Employing the techniques of the density-matrix renormalization group, the effects of long-range interactions and single-ion anisotropy on a variety of correlations are investigated. In order to check the consistency, the fidelity susceptibilities are evaluated across quantum phase transitions. The quantum critical points are faithfully detected and orders of phase transitions are determined. The correlation-length critical exponent is extracted from scaling functions of the fidelity susceptibility. The presence of long-range interactions leads to a quantitative change of the phase boundaries and reduces the order of the phase transition under certain conditions. A direct first-order transition between the periodic N'eel phase and the large-DDD phase occurs for slowly decaying antiferromagnetic interactions.
We study quantum phase transitions in Heisenberg antiferromagnetic chains with a staggered power-law decaying long-range interactions. Employing the density-matrix renormalization group (DMRG) algorithm and the fidelity susceptibility as the criticality measure, we establish more accurate values of quantum critical points than the results obtained from the spin-wave approximation, quantum Monte Carlo, and DMRG in literatures. The deviation is especially evident for strong long-range interactions. We extend isotropic long-range interactions to the anisotropic cases and find that kaleidoscope of quantum phases emerge from the interplay of anisotropy of the long-range exchange interaction and symmetry breaking. We demonstrate nonfrustrating long-range interactions induce the true long-range order in Heisenberg antiferromagnetic chains with a continuous symmetry breaking, lifting the restrictions imposed by the Mermin-Wagner theorem.
We study the fidelity susceptibility of a quantum antiferromagnetic Ising chain with a long-range power-law interaction $1/{r}^{\ensuremath{\alpha}}$ using the large-scale density matrix renormalization group method. We find that the critical adiabatic dimension $\ensuremath{\mu}=2$ and the critical exponent of the correlation length $\ensuremath{\nu}=1$ for arbitrary $\ensuremath{\alpha}>0$, indicating all quantum phase transitions are second-order Ising transitions. In addition, we numerically determine the complete phase diagram for $0<\ensuremath{\alpha}\ensuremath{\le}3$ from the data collapse of the fidelity susceptibility and show that the critical point hc{h}_{c}hc​ changes monotonously with respect to $\ensuremath{\alpha}$. This work will shed light on the nature of phase transitions in the quantum long-range antiferromagnetic Ising chain from a quantum information perspective.
We explore numerically the inverse participation ratios in the ground state of one-dimensional spin-1 XXZXXZXXZ chains with the rhombic single-ion anisotropy. By employing the techniques of density-matrix renormalization group, effects of the rhombic single-ion anisotropy on various information theoretical measures are investigated, such as the fidelity susceptibility, the quantum coherence, and the entanglement entropy. Their relations with the quantum phase transitions are also analyzed. The phase transitions from the YYY-N\'eel phase to the large-Ex{E}_{x}Ex​ or the Haldane phase can be well characterized by the fidelity susceptibility. The second-order derivative of the ground-state energy indicates all the transitions are of second order. We also find that the quantum coherence, the entanglement entropy, the Schmidt gap, and the inverse participation ratios can be used to detect the critical points of quantum phase transitions. Results drawn from these quantum information observables agree well with each other. Finally we provide a ground-state phase diagram as functions of the exchange anisotropy $\mathrm{\ensuremath{\Delta}}$ and the rhombic single-ion anisotropy EEE.
The correlations, entanglement entropy, and fidelity susceptibility are calculated for a one-dimensional spin-1/2 XXZ chain with anisotropic power-law long-range interactions by employing the density matrix renormalization group method. In particular, this long-range interaction is assigned to ferromagnetic for transversal components, while it can be either ferro- or antiferromagnetic for the longitudinal spin component. Two ground-state phase diagrams are established versus the anisotropy of the interactions, which not only changes the phase boundaries of the counterparts with short-range interactions, but also leads to the emergence of exotic phases. We found that the long-range interactions of the zzz component results in a Wigner crystal phase, whereas the transversal one may break a continuous symmetry, resulting in a continuous symmetry-breaking phase.
We study the criticality of a long-range quantum ferromagnetic Ising chain with algebraically decaying interactions $1/{r}^{\ensuremath{\alpha}}$ via the fidelity susceptibility based on the exact diagonalization and the density-matrix renormalization-group techniques. We find that critical exponents change monotonically from the mean-field universality class to the short-range Ising universality class for intermediate $\ensuremath{\alpha}$, which are consistent with recent results obtained from renormalization-group techniques. In addition, we determine the critical values for $1.8\ensuremath{\le}\ensuremath{\alpha}\ensuremath{\le}3$ from the finite-size scaling of the fidelity susceptibility. Our work provides very nice numerical data from the fidelity susceptibility for the quantum long-range ferromagnetic Ising chain.
Long-range interactions can fundamentally reshape the low-energy properties of low-dimensional quantum matter, altering both continuous symmetry breaking and topological phenomena. However, their impact on the quantum criticality separating these regimes remains poorly understood. We determine the ground-state phase diagram and critical properties of the spin-one Heisenberg chain with single-ion anisotropy and staggered antiferromagnetic power-law interactions, using matrix-product state (MPS) calculations complemented by high-order series expansions (pCUT+MC). Such long-range, non-frustrated interactions circumvent the Hohenberg-Mermin-Wagner theorem, thereby stabilizing continuous symmetry breaking (CSB) phases in direct competition with the Haldane phase. We map out the resulting phase diagram and analyze the entanglement entropy scaling behavior in the U(1) and SU(2) CSB phases, finding logarithmic corrections beyond the short-range, universal contributions expected from linearly dispersed Goldstone modes. We further characterize all critical boundaries through finite-size scaling of either the entanglement entropy or the staggered magnetization. In particular, the large-D-to-U(1)-CSB transition exhibits unconventional, continuously varying critical exponents as a function of the long-range decay exponent with a strong dependence on the imposed boundary conditions leading to distinct finite-size scalings for sufficiently long-range potentials. Remarkably, the Haldane-to-U(1)-CSB transition likewise displays unconventional quantum criticality with distinct continuously varying critical exponents. Our work positions this model as a target for near-term atomic platforms with tunable long-range couplings and exhibiting natural single-ion anisotropy, offering a minimal playground for exploring the interplay between long-range interactions, continuous symmetry breaking, and topology.