Kaleidoscope of quantum phases in a long-range interacting spin-1 chain

Abstract

Motivated by recent trapped-ion quantum simulation experiments, we carry out a comprehensive study of the phase diagram of a spin-1 chain with XXZ-type interactions that decay as $1/r^{\alpha}$, using a combination of finite and infinite-size DMRG calculations, spin-wave analysis, and field theory. In the absence of long-range interactions, varying the spin-coupling anisotropy leads to four distinct phases: a ferromagnetic Ising phase, a disordered XY phase, a topological Haldane phase, and an antiferromagnetic Ising phase. If long-range interactions are antiferromagnetic and thus frustrated, we find primarily a quantitative change of the phase boundaries. On the other hand, ferromagnetic (non-frustrated) long-range interactions qualitatively impact the entire phase diagram. Importantly, for $\alpha\lesssim3$, long-range interactions destroy the Haldane phase, break the conformal symmetry of the XY phase, give rise to a new phase that spontaneously breaks a $U(1)$ continuous symmetry, and introduce an exotic tricritical point with no direct parallel in short-range interacting spin chains. We show that the main signatures of all five phases found could be observed experimentally in the near future.Comment: 11 pages, 6 figure

Entanglement Area Laws for Long-Range Interacting Systems

“…While the study of area laws originates from black hole physics [2,3], area laws have received considerable attention recently in the fields of quantum information and condensed matter physics. In particular, area laws are known to be closely related to the velocity of information propagation in quantum lattices [4], quantum critical phenomena [5], bulk-boundary correspondence [6], efficient classical simulation of quantum systems [7], topological order [8], and many-body localization [9].However, the description of many-body systems in terms of local interactions is often only an approximation, and not always a good one; in numerous systems of current interest, ranging from frustrated magnets and spin glasses [10,11] to atomic, molecular, and optical systems [12][13][14][15][16][17], longrangeinteractions are ubiquitous and lead to qualitatively new physics, e.g., giving rise to novel quantum phases and dynamical behaviors [18][19][20][21][22][23][24][25], and enabling speedups in quantum information processing [26][27][28][29][30]. Particles in these systems generally experience interactions that decay algebraically (∼1=r α ) in the distance (r) between them.…”

“…However, the description of many-body systems in terms of local interactions is often only an approximation, and not always a good one; in numerous systems of current interest, ranging from frustrated magnets and spin glasses [10,11] to atomic, molecular, and optical systems [12][13][14][15][16][17], longrangeinteractions are ubiquitous and lead to qualitatively new physics, e.g., giving rise to novel quantum phases and dynamical behaviors [18][19][20][21][22][23][24][25], and enabling speedups in quantum information processing [26][27][28][29][30]. Particles in these systems generally experience interactions that decay algebraically (∼1=r α ) in the distance (r) between them.…”

“…Generalizing these proofs to include long-range interacting Hamiltonians is, however, rather difficult. For example, it is a well-known challenge to generalize Hastings' proof of the area law [35] to higher dimensions [38], and longrange interacting systems are in some sense similar to higherdimensional short-range interacting systems [23,24]. In addition, since ground states of gapped long-range interacting systems can have power-law decaying correlations [39][40][41], one would need to relax the condition of exponentially decaying correlations in the proof of Refs.…”

Edge insulating topological phases in a two-dimensional superconductor with long-range pairing

“…In particular, one-dimensional LR models can host new phases, manifesting striking properties, not present in the SR limit. [15][16][17][21][22][23][24][25][26][27][28][29][30].…”

“…In particular, one-dimensional LR models can host new phases, manifesting striking properties, not present in the SR limit. [15][16][17][21][22][23][24][25][26][27][28][29][30].In spite of these relevant achievements, full comprehension and classification phases emerging from Hamiltonians with LR terms are still not available.In [29] a partial solution to these problems has been discussed, exploiting one-dimensional topological superconductive chains as playgrounds, but inferring nontrivial properties also for LR topological insulators/superconductors in higher dimensions. …”