arXiv subjects

Alexander Seidel

Publications and source records attributed to Alexander Seidel.

At least 55 records · Page 3Linked to original sources

arXiv2012

Entanglement Entropy of Fermi Liquids via Multi-dimensional Bosonization

The logarithmic violations of the area law, i.e. an "area law" with logarithmic correction of the form $S \sim L^{d-1} \log L$, for entanglement entropy are found in both 1D gapless system and for high dimensional free fermions. The purpose of this work is to show that both violations are of the same origin, and in the presence of Fermi liquid interactions such behavior persists for 2D fermion systems. In this paper we first consider the entanglement entropy of a toy model, namely a set of decoupled 1D chains of free spinless fermions, to relate both violations in an intuitive way. We then use multi-dimensional bosonization to re-derive the formula by Gioev and Klich [Phys. Rev. Lett. 96, 100503 (2006)] for free fermions through a low-energy effective Hamiltonian, and explicitly show the logarithmic corrections to the area law in both cases share the same origin: the discontinuity at the Fermi surface (points). In the presence of Fermi liquid (forward scattering) interactions, the bosonized theory remains quadratic in terms of the original local degrees of freedom, and after regularizing the theory with a mass term we are able to calculate the entanglement entropy perturbatively up to second order in powers of the coupling parameter for a special geometry via the replica trick. We show that these interactions do not change the leading scaling behavior for the entanglement entropy of a Fermi liquid. At higher orders, we argue that this should remain true through a scaling analysis.

cond-mat.stat-mech↗

arXiv2012

Gaffnian holonomy through the coherent state method

We analyze the effect of exchanging quasiholes described by Gaffnian quantum Hall trial state wave functions. This exchange is carried out via adiabatic transport using the recently developed coherent state Ansatz. We argue that our Ansatz is justified if the Gaffnian parent Hamiltonian has a charge gap, even though it is gapless to neutral excitations, and may therefore properly describe the adiabatic transport of Gaffnian quasiholes. For nonunitary states such as the Gaffnian, the result of adiabatic transport cannot agree with the monodromies of the conformal block wave functions, and may or may not lead to well-defined anyon statistics. Using the coherent state Ansatz, we find two unitary solutions for the statistics, one of which agrees with the statistics of the non-Abelian spin-singlet state by Ardonne and Schoutens.

cond-mat.mes-hall↗

arXiv2011

Abelian and non-Abelian statistics in the coherent state representation

We further develop an approach to identify the braiding statistics associated to a given fractional quantum Hall state through adiabatic transport of quasiparticles. This approach is based on the notion of adiabatic continuity between quantum Hall states on the torus and simple product states---or "patterns"---in the thin torus limit, together with a suitable coherent state Ansatz for localized quasiholes that respects the modular invariance of the torus. We give a refined and unified account of the application of this method to the Laughlin and Moore-Read states, which may serve as a pedagogical introduction to the nuts and bolts of this technique. Our main result is that the approach is also applicable---without further assumptions---to more complicated non-Abelian states. We demonstrate this in great detail for the level $k=3$ Read-Rezayi state at filling factor $ν=3/2$. These results may serve as an independent check of other techniques, where the statistics are inferred from conformal block monodromies. Our approach has the benefit of giving rise to intuitive pictures representing the transformation of topological sectors during braiding, and allows for a self-consistent derivation of non-Abelian statistics without heavy mathematical machinery.

cond-mat.mes-hall↗

arXiv2011

Gapless excitations in the Haldane-Rezayi state: The thin torus limit

We study the thin torus limit of the Haldane-Rezayi state. Eight of the ten ground states are found to assume a simple product form in this limit, as is known to be the case for many other quantum Hall trial wave functions. The two remaining states have a somewhat unusual thin torus limit, where a "broken" pair of defects forming a singlet is completely delocalized. We derive these limits from the wave functions on the cylinder, and deduce the dominant matrix elements of the thin torus hollow-core Hamiltonians. We find that there are gapless excitations in the thin torus limit. This is in agreement with the expectation that local Hamiltonians stabilizing wave functions associated with non-unitary conformal field theories are gapless. We also use the thin torus analysis to obtain explicit counting formulas for the zero modes of the hollow-core Hamiltonian on the torus, as well as for the parent Hamiltonians of several other paired and related quantum Hall states.

cond-mat.mes-hall↗

arXiv2010

Momentum resolved tunneling into the Pfaffian and anti-Pfaffian edges

We calculate the electron spectral functions at the edges of the Moore-Read Pfaffian and anti-Pfaffian fractional quantum Hall states, in the clean limit. We show that their qualitative differences can be probed using momentum resolved tunneling, thus providing a method to unambiguously distinguish which one is realized in the fractional quantum Hall state observed at filling factor $ν=5/2$. We further argue that edge reconstruction, which may be less important in the first excited Landau level (LL) than in the lowest LL, can also be detected this way if present.

cond-mat.mes-hall↗

arXiv2010

A minimal model of quantized conductance in interacting ballistic quantum wires

We review what we consider to be the minimal model of quantized conductance in a finite interacting quantum wire. Our approach utilizes the simplicity of the equation of motion description to both deal with general spatially dependent interactions and finite wire geometry. We emphasize the role of two different kinds of boundary conditions, one associated with local "chemical" equilibrium in the sense of Landauer, the other associated with screening in the proximity of the Fermi liquid metallic leads. The relation of our analysis to other approaches to this problem is clarified. We then use our formalism to derive a Drude type expression for the low frequency AC-conductance of the finite wire with general interaction profile.

cond-mat.str-el↗

arXiv2010

Spin glassiness and power law scaling in a quasi-triangular spin-1/2 compound

We present data on the magnetic properties of two classes of layered spin S=1/2 antiferromagnetic quasi-triangular lattice materials: $Cu_{2(1-x)}Zn_{2x}(OH)_3NO_3$ ($0 < x < 0.65$) and its long chain organic derivatives $Cu_{2(1-x)}Zn_{2x}(OH)_3(C_7H_{15}COO)\cdot mH_2O$ ($0 < x < 0.29$), where non-magnetic Zn substitutes Cu isostructurally. It is found that the long-chain compounds, even in a clean system in the absence of dilution, $x\!=\!0$, show spin-glass behavior, as evidenced by DC and AC susceptibility, and by time dependent magnetization measurements. A striking feature is the observation of a sharp crossover between two successive power law regimes in the DC susceptibility above the freezing temperature. Specific heat data are consistent with a conventional phase transition in the unintercalated compounds, and glassy behavior in the long chain compunds.

cond-mat.str-el↗

arXiv2010

S-duality constraints on 1D patterns associated with fractional quantum Hall states

Using the modular invariance of the torus, constraints on the 1D patterns are derived that are associated with various fractional quantum Hall ground states, e.g. through the thin torus limit. In the simplest case, these constraints enforce the well known odd-denominator rule, which is seen to be a necessary property of all 1D patterns associated to quantum Hall states with minimum torus degeneracy. However, the same constraints also have implications for the non-Abelian states possible within this framework. In simple cases, including the $ν=1$ Moore-Read state and the $ν=3/2$ level 3 Read-Rezayi state, the filling factor and the torus degeneracy uniquely specify the possible patterns, and thus all physical properties that are encoded in them. It is also shown that some states, such as the "strong p-wave pairing state", cannot in principle be described through patterns.

cond-mat.mes-hall↗

arXiv2009

Linear independence of nearest neighbor valence bond states on the kagome lattice and construction of SU(2)-invariant spin-1/2-Hamiltonian with a Sutherland-Rokhsar-Kivelson quantum liquid ground state

A class of local SU(2)-invariant spin-1/2 Hamiltonians is studied that has ground states within the space of nearest neighbor valence bond states on the kagome lattice. Cases include "generalized Klein'' models without obvious non-valence bond ground states, as well as a "resonating-valence-bond" Hamiltonian whose unique ground states within the nearest neighbor valence bond space are four topologically degenerate "Sutherland-Rokhsar-Kivelson'' (SRK) type wavefunctions, which are expected to describe a gapped $\mathbb{Z}_2$ spin liquid. The proof of this uniqueness is intimately related to the linear independence of the nearest neighbor valence bond states on quite general and arbitrarily large kagome lattices, which is also established in this work. It is argued that the SRK ground states are also unique within the entire Hilbert space, depending on properties of the generalized Klein models. Applications of the strategies developed in this work to other lattice types are also discussed.

cond-mat.str-el↗

arXiv2008

Pfaffian statistics through adiabatic transport in the 1D coherent state representation

Recent work has shown that the low energy sector of certain quantum Hall states is adiabatically connected to simple charge-density-wave patterns that appear, e.g., when the system is deformed into a thin torus. Here it is shown that the patterns emerging in this limit already determine the non-abelian statistics of the $ν=1$ Moore-Read state. Aside from the knowledge of these patterns, the method only relies on the principle of adiabatic continuity, the effectively noncommutative geometry in a strong magnetic field, and topological as well as locality arguments.

cond-mat.mes-hall↗

arXiv2008

Halperin (m, m',n) bilayer quantum Hall states on thin cylinders

The Halperin $(m,m',n)$ bilayer quantum Hall states are studied on thin cylinders. In this limit, charge density wave patterns emerge that are characteristic of the underlying quantum Hall state. The general patterns are worked out from a variant of the plasma analogy. Torus degeneracies are recovered, and for some important special cases a connection to well-known spin chain physics is made. By including interlayer tunneling, we also work out the critical behavior of a possible phase transition between the $(331)$ state and the non-abelian Moore-Read state in the thin cylinder limit.

cond-mat.mes-hall↗

arXiv2007

Domain wall type defects as anyons in phase space

We discuss how the braiding properties of Laughlin quasi-particles in quantum Hall states can be understood within a one-dimensional formalism we proposed earlier. In this formalism the two-dimensional space of the Hall liquid is identified with the phase space of a one-dimensional lattice system, and localized Laughlin quasi-holes can be understood as coherent states of lattice solitons. The formalism makes comparatively little use of the detailed structure of Laughlin wavefunctions, and may offer ways to be generalized to non-abelian states.

cond-mat.mes-hall↗

arXiv2006

The Electronic States of Two Oppositely doped Mott Insulators Bilayers

We study the effect of Coulomb interaction between two oppositely doped low-dimensional tJ model systems. We exactly show that, in the one-dimensional case, an arbitrarily weak interaction leads to the formation of charge neutral electron-hole pairs. We then use two different mean-field theories to address the two-dimensional case, where inter-layer excitons also form and condense. We propose that this results in new features which have no analog in single layers, such as the emergence of an insulating spin liquid phase. Our simple bilayer model might have relevance to the physics of doped Mott insulator interfaces and of the new four layer Ba2CaCu4O8 compound.

cond-mat.str-el↗

arXiv2006

Abelian and Non-abelian Hall Liquids and Charge Density Wave: Quantum Number Fractionalization in One and Two Dimensions

Previously we have demonstrated that, on a torus, the abelian quantum hall liquid is adiabatically connected to a charge density wave as the smaller dimension of the torus is varied. In this work we extend this result to the non-abelian bosonic Hall state. The outcome of these works is the realization that the paradigms of quantum number fractionalization in one dimension (polyacetylene) and two dimensions (fractional quantum Hall effect) are in fact equivalent.

cond-mat.mes-hall↗

arXiv2006

Stabilizing Superconductivity in Nanowires by Coupling to Dissipative Environments

We present a theory for a finite-length superconducting nanowire coupled to an environment. We show that in the absence of dissipation quantum phase slips always destroy superconductivity, even at zero temperature. Dissipation stabilizes the superconducting phase. We apply this theory to explain the "anti-proximity effect" recently seen by Tian et. al. in Zinc nanowires.

cond-mat.supr-con↗

arXiv2005

Incompressible Quantum Liquids and New Conservation Laws

In this letter we investigate a class of Hamiltonians which, in addition to the usual center-of-mass (CM) momentum conservation, also have center-of-mass position conservation. We find that regardless of the particle statistics, the energy spectrum is at least q-fold degenerate when the filling factor is $p/q$, where $p$ and $q$ are coprime integers. Interestingly the simplest Hamiltonian respecting this type of symmetry encapsulates two prominent examples of novel states of matter, namely the fractional quantum Hall liquid and the quantum dimer liquid. We discuss the relevance of this class of Hamiltonian to the search for featureless Mott insulators.

cond-mat.str-el↗

arXiv2005

Phonons in Hubbard ladders studied within the framework of the one-loop renormalization group

We study the effects of phonons in $N$-leg Hubbard ladders within the framework of a one-loop renormalization group. In particular, we explicitly demonstrate that the role of phonons changes {\em qualitatively} even in the simplest two-leg ladder, as compared to the single-chain system where phonons always dominate. Our numerical results suggest that in the spin-gapped phase of the two-leg ladder, the opening of the spin gap by electron-electron interaction also drives the electron-phonon interaction to strong coupling, but in a {\em subdominant} fashion. Therefore, even though the inclusion of phonons does not alter the phase, their subdominant relevance strongly renormalizes some physical properties below the energy scale of the spin gap. This might shine some light on the recent experiments showing an anomalous isotope effects in high-temperature superconductors.

cond-mat.str-el↗

arXiv2005

The Luther-Emery liquid: Spin gap and anomalous flux period

We study the dependence of the ground state energy on an applied Aharonov-Bohm flux $Φ$ for the Luttinger model with large momentum scattering. Employing the method of finite size bosonization, we show that for systems with a spin gap but with gapless charge degrees of freedom, the ground state energy has an exact period of $hc/2e$, i. e. {\em half} a flux quantum, in the limit of large system size $L$. Finite size corrections are found to vanish exponentially in $L$. This behavior is contrasted to that of the spin gapless case, for both even and odd particle number. Generalizations to finite temperature are also discussed.

cond-mat.str-el↗