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.
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.
Antiferromagnetic Hamiltonians with short range, non-frustrating interactions are well known to exhibit long range magnetic order in dimensions d ≥2 but exhibit only quasi-long-range order, with power-law decay of correlations, in d = 1 (for half-integer spin). On the other hand, non-frustrating long range interactions can induce long range order in d = 1. We study Hamiltonians in which the long range interactions have an adjustable amplitude λ, as well as an adjustable power law 1/| x | α , using a combination of quantum Monte Carlo and analytic methods: spin-wave, large N non-linear σ model, and renormalization group methods. We map out the phase diagram in the λ–α plane and study the nature of the critical line separating the phases with long range and quasi-long-range order. We find that this corresponds to a novel line of critical points with continuously varying critical exponents and a dynamical exponent, z <1.
Spin ensembles coupled to optical cavities provide a powerful platform for engineering synthetic quantum matter. Recently, we demonstrated that cavity-mediated infinite-range interactions can induce fast scrambling in a Heisenberg
XXZ spin chain [Phys. Rev. Research 2, 043399 (2020)]. In this paper, we analyze the kaleidoscope of quantum phases that emerge in this system from the interplay of these interactions. Employing both analytical spin-wave theory as well as numerical density-matrix renormalization group calculations, we find that there is a large parameter regime where the continuous
U(1) symmetry of this model is spontaneously broken and the ground state of the system exhibits
XY order. This kind of symmetry breaking and the consequent long-range order is forbidden for short-range interacting systems by the Mermin-Wagner theorem. Intriguingly, we find that the
XY order can be induced by even an infinitesimally weak infinite-range interaction. Furthermore, we demonstrate that in the
U(1) symmetry-broken phase, the half-chain entanglement entropy violates the area law logarithmically. Finally, we discuss a proposal to verify our predictions in state-of-the-art quantum emulators.
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
z 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 spin-
1/2 chains with long-range power-law decaying unfrustrated (bipartite) Heisenberg exchange
Jr∝r−α and multi-spin interactions
Q favoring a valence-bond solid (VBS) ground state. Employing quantum Monte Carlo techniques and Lanczos diagonalization, we analyze order parameters and excited-state level crossings to characterize quantum states and phase transitions in the
(α,Q) plane. For weak
Q and sufficiently slowly decaying Heisenberg interactions (small
α), the system has a long-range-ordered antiferromagnetic (AFM) ground state, and upon increasing
α there is a continuous transition into a quasi long-range ordered (QLRO) critical state of the type in the standard Heisenberg chain. For rapidly decaying long-range interactions, there is transition between QLRO and VBS ground states of the same kind as in the frustrated
J1-
J2 Heisenberg chain. Our most important finding is a direct continuous quantum phase transition between the AFM and VBS states - a close analogy to the 2D deconfined quantum-critical point. In previous 1D analogies the ordered phases both have gapped fractional excitations, and the critical point is a conventional Luttinger Liquid. In our model the excitations fractionalize upon transitioning from the AFM state, changing from spin waves to deconfined spinons. We extract critical exponents at the AFM-VBS transition and use order-parameter distributions to study emergent symmetries. We find emergent O(
4) symmetry of the O(
3) AFM and scalar VBS order parameters. Thus, the order parameter fluctuations exhibit the covariance of a uniaxially deformed O(
4) sphere (an "elliptical" symmetry). This unusual quantum phase transition does not yet have any known field theory description, and our detailed results can serve to guide its construction. We discuss possible experimental realizations.