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arXiv:1110.1815 · Physical Review Letters

Liquid Ground State, Gap, and Excited States of a Strongly Correlated Spin Chain

Igor Lesanovsky

Published Mar 5, 2012• 66 citations
arXivHTMLPDF

Abstract

We present an exact solution of an experimentally realizable and strongly interacting one-dimensional spin system which is a limiting case of a quantum Ising model with long range interaction in a transverse and longitudinal field. Pronounced quantum fluctuations lead to a strongly correlated liquid ground state. For open boundary conditions the ground state manifold consists of four degenerate sectors whose quantum numbers are determined by the orientation of the edge spins. Explicit expressions for the entanglement properties, the exact excitation gap, as well as the exact wave functions for a couple of excited states are analytically derived and discussed. We outline how this system can be experimentally realized in a lattice gas of Rydberg atoms.

DOI
10.1103/physrevlett.108.105301

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We present an exact solution of an experimentally realizable and strongly interacting one-dimensional spin system which is a limiting case of a quantum Ising model with long range interaction in a transverse and longitudinal field. Pronounced quantum fluctuations lead to a strongly correlated liquid ground state. For open boundary conditions the ground state manifold consists of four degenerate sectors whose quantum numbers are determined by the orientation of the edge spins. Explicit expressions for the entanglement properties, the exact excitation gap, as well as the exact wave functions for a couple of excited states are analytically derived and discussed. We outline how this system can be experimentally realized in a lattice gas of Rydberg atoms.
Abstract Quantum spin liquids are elusive but paradigmatic examples of strongly correlated quantum states that are characterized by long-range quantum entanglement. Recently, signatures of a gapped topological Z2{{\mathbb{Z}}}_{2}Z2​ Z 2 spin liquid have been observed in a system of Rydberg atoms; however, the full capability of these platforms to realize quantum spin liquids extends far beyond this state alone. Here, we propose the realization of a different class of spin liquids in a honeycomb array of Rydberg atoms. Exploring the system’s quantum phase diagram using density-matrix renormalization group and exact diagonalization calculations, we identify several density-wave-ordered phases and a trimer spin liquid ground state with an emergent U(1) × U(1) local symmetry. This liquid state originates from superpositions of classical trimer configurations on the dual triangular lattice in the regime where third-nearest-neighbor atoms lie within the Rydberg blockade radius. Finally, we discuss the conditions to enhance the preparation fidelity of this state by a general Rydberg-blockade-based projection mechanism, test the robustness of the trimer spin liquid phase in a range of realistic parameters, and outline methods for its experimental detection.
A model of two interacting one-dimensional fermion systems (``Luttinger liquids'') coupled by single-particle hopping is investigated. Bosonization allows a number of exact statements to be made. In particular, for forward scattering only, the model contains two massless boson sectors and an Ising-type critical sector. For general repulsive interactions, there is a spin excitation gap and either d-type pairing or orbital antiferromagnetic fluctuations dominate. It is argued that the same behavior is also found for strong interactions. A possible scenario for the crossover to a Fermi liquid in a many-chain system is discussed. \textcopyright{} 1996 The American Physical Society.
We investigate a ladder system with two inequivalent legs, namely, a Hubbard chain and a one-dimensional electron gas. Analytical approximations, the density-matrix renormalization group method, and continuous-time quantum Monte Carlo simulations are used to determine ground-state properties, gaps, and spectral functions of this system at half-filling. Evidence for the existence of four different phases as a function of the Hubbard interaction and the rung hopping is presented. First, a Luttinger liquid exists at very weak interchain hopping. Second, a Kondo-Mott insulator with spin and charge gaps induced by an effective rung exchange coupling is found at moderate interchain hopping or strong Hubbard interaction. Third, a spin-gapped paramagnetic Mott insulator with incommensurate excitations and pairing of doped charges is observed at intermediate values of the rung hopping and the interaction. Fourth, the usual correlated band insulator is recovered for large rung hopping. We show that the wave numbers of the lowest single-particle excitations are different in each insulating phase. In particular, the three gapped phases exhibit markedly different spectral functions. We discuss the relevance of asymmetric two-leg ladder systems as models for atomic wires deposited on a substrate.
We describe a coupled-chain construction for chiral spin liquids in two-dimensional spin systems. Starting from a one-dimensional zigzag spin chain and imposing SU(2) symmetry in the framework of non-Abelian bosonization, we first show that our approach faithfully describes the low-energy physics of an exactly solvable model with a three-spin interaction. Generalizing the construction to the two-dimensional case, we obtain a theory that incorporates the universal properties of the chiral spin liquid predicted by Kalmeyer and Laughlin: charge-neutral edge states, gapped spin-1/2 bulk excitations, and ground-state degeneracy on the torus signaling the topological order of this quantum state. In addition, we show that the chiral spin liquid phase is more easily stabilized in frustrated lattices containing corner-sharing triangles, such as the extended kagome lattice, than in the triangular lattice. Our field-theoretical approach invites generalizations to more exotic chiral spin liquids and may be used to assess the existence of the chiral spin liquid as the ground state of specific lattice systems.
We describe a coupled-chain construction for chiral spin liquids in two-dimensional spin systems. Starting from a one-dimensional zigzag spin chain and imposing SU(2) symmetry in the framework of non-Abelian bosonization, we first show that our approach faithfully describes the low-energy physics of an exactly solvable model with a three-spin interaction. Generalizing the construction to the two-dimensional case, we obtain a theory that incorporates the universal properties of the chiral spin liquid predicted by Kalmeyer and Laughlin: charge-neutral edge states, gapped spin-1/2 bulk excitations, and ground state degeneracy on the torus signalling the topological order of this quantum state. In addition, we show that the chiral spin liquid phase is more easily stabilized in frustrated lattices containing corner-sharing triangles, such as the extended kagome lattice, than in the triangular lattice. Our field theoretical approach invites generalizations to more exotic chiral spin liquids and may be used to assess the existence of the chiral spin liquid as the ground state of specific lattice systems.
We study the phase diagram of the spin-1/2 XXZ Heisenberg chain in a staggered magnetic field. An exact solution is obtained along the phase boundary, where the exchange anisotropy and the staggered-field strength satisfy an exact analytical relation, yielding a highly degenerate manifold of ground states with off-diagonal long-range order. We demonstrate that these exact ground states lie on the boundary between the ferromagnetic phase and a gapless Luttinger liquid phase. Upon further decreasing the anisotropy, the gapless phase eventually gives way to a gapped quantum-disordered phase. Large-scale density-matrix renormalization group calculations confirm this phase structure and indicate that the transition across the exact boundary is of first order. Our results provide an exact benchmark for understanding quantum phase transitions driven by staggered magnetic fields in one-dimensional quantum spin systems.