49 research outputs found
Scattering particles in quantum spin chains
A variational approach for constructing an effective particle description of
the low-energy physics of one-dimensional quantum spin chains is presented.
Based on the matrix product state formalism, we compute the one- and
two-particle excitations as eigenstates of the full microscopic Hamiltonian. We
interpret the excitations as particles on a strongly-correlated background with
non-trivial dispersion relations, spectral weights and two-particle S matrices.
Based on this information, we show how to describe a finite density of
excitations as an interacting gas of bosons, using its approximate
integrability at low densities. We apply our framework to the Heisenberg
antiferromagnetic ladder: we compute the elementary excitation spectrum and the
magnon-magnon S matrix, study the formation of bound states and determine both
static and dynamic properties of the magnetized ladder.Comment: published versio
Excitations and the tangent space of projected entangled-pair states
We develop tangent space methods for projected entangled-pair states (PEPS)
that provide direct access to the low-energy sector of strongly-correlated
two-dimensional quantum systems. More specifically, we construct a variational
ansatz for elementary excitations on top of PEPS ground states that allows for
computing gaps, dispersion relations, and spectral weights directly in the
thermodynamic limit. Solving the corresponding variational problem requires the
evaluation of momentum transformed two-point and three-point correlation
functions on a PEPS background, which we can compute efficiently by using a
contraction scheme. As an application we study the spectral properties of the
magnons of the Affleck-Kennedy-Lieb-Tasaki model on the square lattice and the
anyonic excitations in a perturbed version of Kitaev's toric code
S matrix from matrix product states
We use the matrix product state formalism to construct stationary scattering
states of elementary excitations in generic one-dimensional quantum lattice
systems. Our method is applied to the spin-1 Heisenberg antiferromagnet, for
which we calculate the full magnon-magnon S matrix for arbitrary momenta and
spin, the two-particle contribution to the spectral function and the
magnetization curve. As our method provides an accurate microscopic
representation of the interaction between elementary excitations, we envisage
the description of low-energy dynamics of one-dimensional spin chains in terms
of these particlelike excitations.Comment: Improved version, extra supplemental materia
Approaching the Kosterlitz-Thouless transition for the classical XY model with tensor networks
We apply variational tensor-network methods for simulating the Kosterlitz-Thouless phase transition in the classical two-dimensional XY model. In particular, using uniform matrix product states (MPS) with non-Abelian O(2) symmetry, we compute the universal drop in the spin stiffness at the critical point. In the critical low-temperature regime, we focus on the MPS entanglement spectrum to characterize the Luttinger-liquid phase. In the high-temperature phase, we confirm the exponential divergence of the correlation length and estimate the critical temperature with high precision. Our MPS approach can be used to study generic two-dimensional phase transitions with continuous symmetries
Hole Spectral Function of a Chiral Spin Liquid in the Triangular Lattice Hubbard Model
Quantum spin liquids are fascinating phases of matter, hosting fractionalized
spin excitations and unconventional long-range quantum entanglement. These
exotic properties, however, also render their experimental characterization
challenging, and finding ways to diagnose quantum spin liquids is therefore a
pertinent challenge. Here, we numerically compute the spectral function of a
single hole doped into the half-filled Hubbard model on the triangular lattice
using techniques based on matrix product states. At half-filling the system has
been proposed to realize a chiral spin liquid at intermediate interaction
strength, surrounded by a magnetically ordered phase at strong interactions and
a superconducting/metallic phase at weak interactions. We find that the spectra
of these phases exhibit distinct signatures. By developing appropriate parton
mean-field descriptions, we gain insight into the relevant low-energy features.
While the magnetic phase is characterized by a dressed hole moving through the
ordered spin background, we find indications of spinon dynamics in the chiral
spin liquid. Our results suggest that the hole spectral function, as measured
by angle-resolved photoemission spectroscopy, provides a useful tool to
characterize quantum spin liquids.Comment: 8 pages, 6 figures (published version
A gapped SU(3) spin liquid with Z_3 topological order
We construct a topological spin liquid (TSL) model on the kagome lattice,
with SU(3) symmetry with the fundamental representation at each lattice site,
based on Projected Entangled Pair States (PEPS). Using the PEPS framework, we
can adiabatically connect the model to a fixed point model (analogous to the
dimer model for Resonating Valence Bond states) which we prove to be locally
equivalent to a quantum double model. Numerical study of the
interpolation reveals no sign of a phase transition or long-range order,
characterizing the model conclusively as a gapped TSL. We further study the
entanglement spectrum of the model and find that while it is gapped, it
exhibits branches with vastly different velocities, with the slow branch
matching the counting of a chiral CFT, suggesting that it can be
deformed to a model with chiral entanglement spectrum.Comment: 5 pages. Accepted versio