Searcharxiv⌕ Search

arXiv subjects

Martin Greiter

Publications and source records attributed to Martin Greiter.

At least 55 records · Page 3Linked to original sources
arXiv2012

Parent Hamiltonian for the non-Abelian chiral spin liquid

We construct a parent Hamiltonian for the family of non-Abelian chiral spin liquids proposed recently by two of us [PRL 102, 207203 (2009)], which includes the Abelian chiral spin liquid proposed by Kalmeyer and Laughlin, as the special case S=1/2. As we use a circular disk geometry with an open boundary, both the annihilation operators we identify and the Hamiltonians we construct from these are exact only in the thermodynamic limit.

cond-mat.str-el↗
arXiv2011

A family of spin-S chain representations of SU(2)_k Wess-Zumino-Witten models

We investigate a family of spin-S chain Hamiltonians recently introduced by one of us. For S=1/2, it corresponds to the Haldane-Shastry model. For general spin S, we find indication that the low-energy theory of these spin chains is described by the SU(2)_k Wess-Zumino-Witten model with coupling k=2S. In particular, we investigate the S=1 model whose ground state is given by a Pfaffian for even number of sites N. We reconcile aspects of the spectrum of the Hamiltonian for arbitrary N with trial states obtained by Schwinger projection of two Haldane-Shastry chains.

cond-mat.str-el↗
arXiv2011

Mapping of Parent Hamiltonians: from Abelian and non-Abelian Quantum Hall States to Exact Models of Critical Spin Chains

This monograph introduces an exact model for a critical spin chain with arbitrary spin S, which includes the Haldane--Shastry model as the special case S=1/2. While spinons in the Haldane--Shastry model obey abelian half-fermi statistics, the spinons in the general model introduced here obey non-abelian statistics. This manifests itself through topological choices for the fractional momentum spacings. The general model is derived by mapping exact models of quantized Hall states onto spin chains. The book begins with pedagogical review of all the relevant models including the non-abelian statistics in the Pfaffian Hall state, and is understandable to every student with a graduate course in quantum mechanics.

cond-mat.str-el↗
arXiv2011

Fractional spin liquid hierarchy for spin S antiferromagnets

We propose a hierarchy of spin liquids with spin S, which are generated via a Schwinger boson projection from 2S (Abelian) chiral spin liquids with S=1/2. We argue that the P and T invariant liquids we construct for integer spin S support SU(2) level k=S non-Abelian statistics. We conjecture that these spin liquids serve as paradigms for antiferromagnets which are disordered through mobile charge carriers.

cond-mat.str-el↗
arXiv2011

Landau Level Quantization on the Sphere

It is well established that the Hilbert space for charged particles in a plane subject to a uniform magnetic field can be described by two mutually commuting ladder algebras. We propose a similar formalism for Landau level quantization involving two mutually commuting SU(2) algebras.

cond-mat.str-el↗
arXiv2011

Magnetic Excitations in the Site-Centered Stripe Phase: Spin Wave Theory of Coupled Three-Leg Ladders

The success of models of coupled two-leg spin ladders in describing the magnetic excitation spectrum of La_{2-x}Ba_xCuO_4 had been interpreted previously as evidence for bond-centered stripes. In a recent article, however, we have determined the magnetic coupling induced by the charge stripes between bond- or site-centered spin stripes modeled by two- or three-leg ladders, respectively. We found that only the site-centered models order. We further indicated excellent agreement of a fully consistent analysis of coupled three-leg ladders using a spin wave theory of bond with the experimental data. Here, we provide a full and detailed account of this analysis.

cond-mat.supr-con↗
arXiv2010

Evidence for site-centered stripes from magnetic excitations in CuO superconductors

The success of models of coupled two-leg spin ladders in describing the magnetic excitation spectrum of La_[2-x]Ba_xCuO_4 has been widely interpreted as evidence for bond-centered stripes. Here, we determine the magnetic coupling induced by the charge stripes between bond- or site-centered spin stripes modeled by two- or three-leg ladders, respectively. We find that only the site-centered models order. We further report excellent agreement of a fully consistent analysis of coupled three-leg ladders using a spin wave theory of bond operators with the experiment.

cond-mat.str-el↗
arXiv2009

Confinement in a Quantum Magnet

The elementary excitations of a state of matter consisting of large collection of interacting particles can be very different from the original particles. In the most interesting examples, the particles effectively decompose into smaller constituent particles, which only carry a fraction of their quantum numbers. When these constituents are free, as in fractionally quantised Hall states, it is conceptually clear how to observe them. But what if they are confined, as it might be the case in spin liquids hypothesised to describe high Tc superconductors?

cond-mat.str-el↗
arXiv2009

Parent Hamiltonian for the Chiral Spin Liquid

We present a method for constructing parent Hamiltonians for the chiral spin liquid. We find two distinct Hamiltonians for which the chiral spin liquid on a square lattice is an exact zero-energy ground state. We diagonalize both Hamiltonians numerically for 16-site lattices, and find that the chiral spin liquid, modulo its two-fold topological degeneracy, is indeed the unique ground state for one Hamiltonian, while it is not unique for the other.

cond-mat.str-el↗
arXiv2009

Spontaneous Parity Violation in a Quantum Spin Chain

We report on a spontaneous breakdown of parity in the ground state of a spin Hamiltonian involving nearest-neighbor interactions. This occurs for a one-dimensional model where spins transform under the gauge field representation of QCD, the eight-dimensional adjoint representation of SU(3). The ground state spontaneously violates parity and is two-fold degenerate. In addition, the model possesses a non-vanishing topological string order parameter which we explicate analytically.

cond-mat.str-el↗
arXiv2009

Non-Abelian Statistics in a Quantum Antiferromagnet

We propose a novel spin liquid state for a spin S=1 antiferromagnet in two dimensions. The ground state violates P and T, is a spin-singlet, and is fully invariant under the lattice symmetries. The spinon and holon excitations are deconfined and obey non-abelian statistics. We present preliminary numerical evidence that the universality class of this topological liquid can be stabilized by a local Hamiltonian involving three-spin interactions. We conjecture that spinons in spin liquids with spin larger than 1/2 obey non-abelian statistics in general.

cond-mat.str-el↗
arXiv2008

Exact models for trimerization and tetramerization in spin chains

We present exact models for an antiferromagnetic S=1 spin chain describing trimerization as well as for an antiferromagnetic S=3/2 spin chain describing tetramerization. These models can be seen as generalizations of the Majumdar-Ghosh model. For both models, we provide a local Hamiltonian and its exact three- or four-fold degenerate ground state wavefunctions, respectively. We numerically confirm the validity of both models using exact diagonalization and discuss the low lying excitations.

cond-mat.str-el↗
arXiv2007

Numerical analysis of three-band models for CuO planes as candidates for a spontaneous T violating orbital current phase

Recently, we have numerically evaluated the current-current correlation function for the ground states of three-band models for the CuO planes of high-Tc superconductors at hole doping x=1/8 using systems with 24 sites and periodic boundary conditions. In this article, the numerical analysis is explicated in detail and extended to a wider range of parameters. Our results show no evidence for the time-reversal symmetry violating current patterns recently proposed by Varma. If such current patterns exist, our results indicate that the energy associated with the loop currents must be smaller than 5 meV per link even if the on-site chemical potential on the oxygen sites, which is generally assumed to be of the order of 3.6 eV, is taken to zero, as advocated by Varma. We also vary the inter-atomic Coulomb repulsion scale and find only a weak dependence on this parameter. So while our studies do not rule out the existence of such current patterns, they do rule out that quantum critical fluctuations of these patterns are responsible for phenomena occurring at significantly higher energies such as the superconductivity or the anomalous properties observed in the strange metal phase provided the CuO superconductors are adequately described by any of the three-band models discussed.

cond-mat.supr-con↗
arXiv2007

Statistical Phases and Momentum Spacings for One-Dimensional Anyons

Anyons and fractional statistics are by now well established in two-dimensional systems. In one dimension, fractional statistics has been established so far only through Haldane's fractional exclusion principle, but not via a fractional phase the wave function acquires as particles are interchanged. At first sight, the topology of the configuration space appears to preclude such phases in one dimension. Here we argue that the crossings of one-dimensional anyons are always unidirectional, which makes it possible to assign phases consistently and hence to introduce a statistical parameter theta. The fractional statistics then manifests itself in fractional spacings of the single-particle momenta of the anyons when periodic boundary conditions are imposed. These spacings are given by Delta p = 2 pi hbar/L (|theta|/pi+non-negative integer) for a system of length L. This condition is the analogue of the quantisation of relative angular momenta according to l_z=hbar(-theta/pi+2integer) for two-dimensional anyons.

quant-ph↗
arXiv2007

Many-spinon states and the secret significance of Young tableaux

We establish a one-to-one correspondence between the Young tableaux classifying the total spin representations of N spins and the exact eigenstates of the the Haldane-Shastry model for a chain with N sites classified by the total spins and the fractionally spaced single-particle momenta of the spinons.

cond-mat.str-el↗
arXiv2007

Valence bond solids for SU(n) spin chains: exact models, spinon confinement, and the Haldane gap

To begin with, we introduce several exact models for SU(3) spin chains: (1) a translationally invariant parent Hamiltonian involving four-site interactions for the trimer chain, with a three-fold degenerate ground state. We provide numerical evidence that the elementary excitations of this model transform under representation 3bar of SU(3) if the original spins of the model transform under rep. 3. (2) a family of parent Hamiltonians for valence bond solids of SU(3) chains with spin reps. 6, 10, and 8 on each lattice site. We argue that of these three models, only the latter two exhibit spinon confinement and hence a Haldane gap in the excitation spectrum. We generalize some of our models to SU(n). Finally, we use the emerging rules for the construction of VBS states to argue that models of antiferromagnetic chains of SU(n) spins in general possess a Haldane gap if the spins transform under a representation corresponding to a Young tableau consisting of a number of boxes λwhich is divisible by n. If λand n have no common divisor, the spin chain will support deconfined spinons and not exhibit a Haldane gap. If λand n have a common divisor different from n, it will depend on the specifics of the model including the range of the interaction.

cond-mat.str-el↗