Topological phases and topological entropy of two-dimensional systems with finite correlation length

by Stefanos Papanikolaou, Kumar S. Raman and Eduardo Fradkin

This nicely written paper begins with a survey of the current understanding of topological entropy. They then proceed to compute it in three new cases involving a finite correlation length, going beyond the idealized models studied in the past.

The topological entropy is a universal subleading correction of the non-universal von Neumann entropy. Levin and Wen and Kitaev and Preskil show how this subleading correction may be extracted in the limit of a small correlation length and that it is related to the "quantum dimension" of the topological phase.

The authors of the current paper demonstrate that a finite correlation length introduces corrections to this subleading term as expected from geometry effects (see last equation of section III, for example). The therefore verify explicitly that the topological entropy is universal.

Antiphase Stripe Order as the Origin of Electron Pockets Observed in 1/8-Hole-Doped Cuprates

Recent magneto-transport experiments in very large magnetic fields reveal Shubnikov-de Haas oscillations in the "normal" state of YBCO (see for example Shubnikov-de Haas oscillations in YBa_2Cu_4O_8). The magnetic fields, on the order of 60T suppress the superconductivity allowing a study of the normal state down to low temperatures. The simplest interpretation of the observed "quantum" oscillations, as they are sometimes called, is that they correspond to the formation of four small Fermi surfaces called "pockets".

In this paper, the authors consider the breakup of a large Fermi surface due to the presence of "anti-phase stripe" ordering. After D-wave superconductivity and antiferromagnetism, this ordering is the next most well established in the cuprates, known to suppress superconductivity near x=1/8 doping in LSCO and LBCO. They show that a robust region of their parameter space correspond to electron-like pockets, which are not easily explained by pure antiferromagnetic order. Thus they propose that this anti-phase stripe ordering is induced in YBCO at finite magnetic field and that its inflouence may be generic to all cuprates.

Supersolid and devil's staircase of hardcore bosons on anisotropic triangular lattice

by Sergei V. Isakov, Hong-Chi Chien, Jian-Jheng Wu, Yung-Chung Chen, Chung-Hou Chung, Krishnendu Sengupta, Yong Baek Kim

In connection with the previous post, today an interesting paper appeared studying the supersolid phase of hardcore bosons on the anisotropic triangular lattice. Remarkably, as the anisotropy is increased, these authors have discovered a series of first order phase transition between supersolid phases with different \vec Q. Based on a Quantum Monte Carlo study, these authers find that the \vec Q of each of the successive phases take on rational fractions and extrapolate from this result that all rational fractions may be explored if they could study the thermodynamic limit. Such a series of phase transitions is called a devil's staircase and is a rare occurance in quantum many-body physics (they only other case I know of is occurs in the quantum dimer model).

Superfluids and Supersolids on Frustrated 2D Lattices

by Ganpathy Murthy, Daniel Arovas, Assa Auerbach

Today I hand a nice conversation with Erhai who pointed the interesting subject of supersolids on triangular and kagome lattices. What exactly is a supersolid phase, you may ask? Erhai had a nice answer: a phase in which bosons both crystalize and condense into a superfluid. Unfortunately, simple models that exhibit a supersolid phase on the square lattice are unstable towards phase separating into regions of solid and superfluid order (at least according to direct numerical solution of the models for small systems).

This paper raises the possibility that a supersolid phase can arise out of a frustration, a result that is supported by recent numerical studies on the triangular lattice. This is a remarkable result for it implies a type of "order from disorder" arising from quantum fluctuations in a model that can be understood by both simple mean field methods and powerful numerical techniques.

Modeling the Fermi arc in underdoped cuprates

by M. R. Norman, A. Kanigiel, M. Randeria, U. Chatterjee, J. C. Campuzano

This article surveys the current state of our understanding of the "Fermi arcs" observed in the pseudogap phase in the cuprates. If you think about it for a moment, why would a Fermi surface simple end? There is, of course, the possibility that the arc is really a bannan shaped pocket, so that it forms a closed surface as predicted from weak coupling models. But there is also the possibility that this pseudogap phase requires new and creative ideas that take us well beyond Fermi liquid theory, to think of the strongly correlated regime in terms of new paradigms.

By following a modeling approach, wherein different theories give rise to certain simple forms for the fermion green function, this paper compares current theories of Fermi arcs with experiment. While no theory stands out as a clear winner, they are able to rule out some theories. By dividing the collection of theories into what they call q=0 theories (which are more or less theories of liquids) and q \neq 0 theories (theories where translational symmetry is broken, such as SDW, CDW, etc.) they conclude that those among the q \neq 0 set do not adequately compare with the data. While perhaps not so surprising, this article does a nice job of surving the current situation and provides a nice place to start for those interested in the subject.

An exact chiral spin liquid with non-Abelian anyons

by Hong Yao, Steven A. Kivelson

This is another interesting development in the field of topological quantum computing that came out during the Aspen work shop on the subject this summer. In the Kitaev model, a bizarre but exactly solvable spin model on the honeycombe lattice, a topological phase with non-abelian topological defects (vortices) can arise in the presence of a magnetic field. Unfortunately, a magnetic field spoils the exact solvability of the model leaving us only with a perturbative understanding of this interesting phase.

Here, Yao and Kivelson extend the Kitaev model to a lattice that is somewhere in between a honeycombe and a kagome lattice. They show that the topological phase with non-abelian excitations can arise spontaneously in this extended model. Furthermore, they were able to analyse the phase exactly. In addition, they make use of a recent discovery by Feng, Zhang and Xiang who solved the Kitaev model by a simple Jordan-Wigner transformation which converts the model into spinless fermions that in turn reduces to a model of free Marajona (charge neutral) fermions. As a result, Yao and Kivelson are able to explain their results in a very simple and intuitive language.

Engineering exotic phases for topologically-protected quantum computation by emulating quantum dimer models

by A. Fabricio Albuquerque, Helmut G. Katzgraber, Matthias Troyer, Gianni Blatter

While at Aspen this summer, I had the opportunity to hear Matthias Troyer introduce this interesting study on the possibility of simply engineering a topological quantum computer. In this paper, they consider the quantum dimer model on a triangular lattice (see Moessner and Sondhi, 2000) which is known to have a gapped resonating dimer (valence bond) phase with topologically protected degenerate ground states (that could be used to store a 0 or a 1, for example). They study a "microscopic" model of a system of Josephson junctions engineered in such a way as to produce the mentioned quantum dimer model at low energies. Their central result, however, is negative: under the best circumstances, this system needs to be at or below 1 mK in order to successfully operate as a storage device of a quantum bit. The lesson to be drawn is then quite simple: to engineer such a phase, one needs to start from a system with very large energy scales so that its low energy sector can still be studied at accessible temperatures.

I find in particular that I am drawn to their numerical technique called CORE. This technique projects the lowest lying energy states of an exactly diagonalized hamiltonian onto a hoped for low energy subspace. The quality of the projection is then analyzed and if successful, provides strong evidence that a particular low energy effective model truly captures the low lying excitations of a particular system. This seems to be a particularly effective analysis of an exact diagonalization study.