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Martin Greiter

Publications and source records attributed to Martin Greiter.

At least 73 records · Page 4Linked to original sources
arXiv2007

Exact results for SU(3) spin chains: trimer states, valence bond solids, and their parent Hamiltonians

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 a Haldane gap in the excitation spectrum.

cond-mat.str-el↗
arXiv2007

No evidence for spontaneous orbital currents in finite size studies of three-band models for CuO planes

We have numerically evaluated the current-current correlations for three-band models of the CuO planes in high-T_c superconductors at hole doping x=1/8. The results show no evidence for the orbital current patterns proposed by Varma. If such patterns exist, the associated energy is estimated to be smaller than 5 meV per link even if epsilon_p-epsilon_d=0. Assuming that the three-band models are adequate, quantum critical fluctuations of such patterns hence cannot be responsible for phenomena occurring at significantly higher energies, such as superconductivity or the anomalous properties of the pseudogap phase.

cond-mat.supr-con↗
arXiv2006

Charge excitations in SU(n) spin chains: exact results for the 1/r^2 model

We study the one- and two-holon excitations of the SU(3) Kuramoto-Yokoyama model on the level of explicit wave functions, and generalize the calculations to the case of SU(n). We obtain the exact energies and the single holon momenta, which we find fractionally spaced according to fractional statistics with statistical parameter g=1/n.

cond-mat.str-el↗
arXiv2006

Exact two-holon wave functions in the Kuramoto-Yokoyama model

We construct the explicit two-holon eigenstates of the SU(2) Kuramoto-Yokoyama model at the level of explicit wave functions. We derive the exact energies and obtain the individual holon momenta, which are quantized according to the half-Fermi statistics of the holons.

cond-mat.str-el↗
arXiv2006

Coloron excitations of the SU(3) Haldane--Shastry model

In a recent publication, we proposed two possible wave functions for the elementary excitations of the SU(3) Haldane--Shastry model (HSM), but argued on very general grounds that only one or the other can be a valid excitation. Here we provide the explicit details of our calculation proving that the wave function describing a coloron excitation which transforms according to representation $\bar{3}$ under SU(3) rotations if the spins of the original model transform according to representation 3, is exact. We further provide an explicit construction of the exact color-polarized two-coloron eigenstates, and thereby show that colorons are free but that their relative momentum spacings are shifted according to fractional statistics with parameter $g=2/3$. We evaluate the SU(3) spin currents. Finally, we interpret our results within the framework of the asymptotic Bethe Ansatz and generalize some of them to the case of SU($n$).

cond-mat.str-el↗
arXiv2005

Complementary colors of colorons: the elementary excitations of the SU(3) Haldane--Shastry model

We propose two possible trial wave functions for the elementary excitations of the SU(3) Haldane--Shastry model, but then argue on very general grounds that only one or the other can be a valid excitation. We then prove explicitly that the trial wave function describing a coloron excitation which transforms according to representation $\bar{3}$ under SU(3) rotations if the spins of the original model transform according to representation 3, is exact. If a basis for the spins on the chain is spanned by the colors blue, red, and green, a basis for the coloron excitations is hence given by the complementary colors yellow, cyan, and magenta. We obtain the dispersion and the exclusion statistics among polarized colorons. Furthermore, we compare our results with the asymptotic Bethe Ansatz and discuss the generalization to SU($n$).

cond-mat.str-el↗
arXiv2005

Is electromagnetic gauge invariance spontaneously violated in superconductors?

We aim to give a pedagogical introduction to those elementary aspects of superconductivity which are not treated in the classic textbooks. In particular, we emphasize that global U(1) phase rotation symmetry, and not gauge symmetry, is spontaneously violated, and show that the BCS wave function is, contrary to claims in the literature, fully gauge invariant. We discuss the nature of the order parameter, the physical origin of the many degenerate states, and the relation between formulations of superconductivity with fixed particle numbers vs. well defined phases. We motivate and to some extend derive the effective field theory at low temperatures, explore symmetries and conservation laws, and justify the classical nature of the theory. Most importantly, we show that the entire phenomenology of superconductivity essentially follows from the single assumption of a charged order parameter field. This phenomenology includes Anderson's characteristic equations of superfluidity, electric and magnetic screening, the Bernoulli Hall effect, the balance of the Lorentz force, as well as the quantum effects, in which Planck's constant manifests itself through the compactness of the U(1) phase field. The latter effects include flux quantization, phase slippage, and the Josephson effect.

cond-mat.supr-con↗
arXiv2004

Contemplations on Dirac's equation in quaternionic coordinates

A formulation of Dirac's equation using complex-quaternionic coordinates appears to yield an enormous gain in formal elegance, as there is no longer any need to invoke Dirac matrices. This formulation, however, entails several peculiarities, which we investigate and attempt to interpret.

math-ph↗
arXiv2004

Is there an attraction between spinons in the Haldane--Shastry model?

While the Bethe Ansatz solution of the Haldane--Shastry model appears to suggest that the spinons represent a free gas of half-fermions, Bernevig, Giuliano, and Laughlin (BGL) (cond-mat/0011069, cond-mat/0011270) have concluded recently that there is an attractive interaction between spinons. We argue that the dressed scattering matrix obtained with the asymptotic Bethe Ansatz is to be interpreted as the true and physical scattering matrix of the excitations, and hence, that the result by BGL is inconsistent with an earlier result by Essler (cond-mat/9406081). We critically re-examine the analysis of BGL, and conclude that there is no interaction between spinons or spinons and holons in the Haldane--Shastry model.

cond-mat.str-el↗
arXiv2002

S=1 Spin Liquids: Broken Discrete Symmetries Restored

We introduce a novel kind of spin liquid, the spin 1 chirality liquid, which provides a generic paradigm for a disordered spin 1 antiferromagnet in two dimensions. It supports spinon and holon excitations, which carry a chirality quantum number. These excitations obey half-fermi statistics. The sign of the statistical parameter is determined by the chirality. The spin 1 chirality liquid is the first example of a two dimensional quantum state which supports excitations with fractional statistics but does not violate P or T.

cond-mat.str-el↗
arXiv1998

Fictitious flux confinement: magnetic pairing in coupled spin chains or planes

The spinon and holon excitations of two-leg Heisenberg or lightly doped t-J ladders are shown to be bound in pairs by string confinement forces given approximately by the antiferromagnetic exchange energy across the rungs. These forces originate from the fictitious flux tubes associated with the half-fermi statistics of the excitations. It is conjectured that similar confinement forces, determined by the antiferromagnetic exchange energy across the layers, are responsible for the spin gap and the pairing of charge carriers in CuO superconductors.

cond-mat↗
arXiv1997

Greiter replies to Demler, Zhang, Meixner, and Hanke

In a comment on my recent manuscript on the pi-particle [cond-mat/9705049], Demler et al. [cond-mat/9705191] argued that there is a correction to the chemical potential which enters the expression for the energy of the pi-particle given in [Demler and Zhang, Phys. Rev. Lett. 77, 4126 (1995)]. This is shown to be incorrect. I further offer an interpretation for the low-energy resonances observed by Meixner et al. [cond-mat/9701217] in the pi-pi correlation function in a finite-size Hubbard cluster at low electron densities.

cond-mat.supr-con↗
arXiv1997

Is the pi-particle responsible for the 41 meV peak in YBa_2Cu_3O_7?

It is argued that there is no low-energy resonance associated with the pi-operators introduced by Demler and Zhang. This implies that the Hubbard model does not possess an approximate SO(5) symmetry generated by these operators. Recent finite-size studies are re-interpreted accordingly.

cond-mat.supr-con↗
arXiv1996

Quantum Hall quarks or Short distance physics of quantized Hall fluids

In order to obtain a local description of the short distance physics of fractionally quantized Hall states for realistic (e.g. Coulomb) interactions, I propose to view the zeros of the ground state wave function, as seen by an individual test electron from far away, as particles. I then present evidence in support of this interpretation, and argue that the electron effectively decomposes into quark-like constituent particles of fractional charge.

cond-mat↗