The study of physical properties condensed phases of matter, including solids and liquids.

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276 views

Quasi 1D insulators with strong spin-orbital interaction

We know that the spin-1 chain realizes the Haldane phase which is an example of symmetry protected topological (SPT) phases (ie short-range entangled phases with symmetry). The Haldane phase is ...
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325 views

Some questions about anyons?

(1) As we know, we have theories of second quantization for both bosons and fermions. That is, let $W_N$ be the $N$ identical particle Hilbert space of bosons or fermions, then the "many particle" ...
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314 views

How does Haldane conjecture follow from the topological $\Theta$ term

The one dimensional SU(2) Heisenberg quantum spin chain is known to be described by the 1+1d O(3) nonlinear $\sigma$ model with a $\Theta$ term, following the action ...
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651 views

Griffiths phase

What are Griffiths effects in the context of condensed matter physics? From a cursory examination of the literature I've gathered the following: it seems that ordered systems have a "clean" critical ...
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320 views

Is the “particle number” of “electrons” well defined in Wen's string-net theory of elementary particles?

According to professor Wen's string-net theory, electrons can be viewed as the elementary excitations of string-net objects. Just like the phonons and magnons are the elementary excitations of ...
7
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274 views

Descent equation and anomaly polynomial

I am just reading Ryu, Moore and Ludwig's paper on classifications of topological insulators and quantum anomaly. They are trying to relate the quantum anomaly as a signal of the presence of a ...
6
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253 views

When can we take the Brillouin zone to be a sphere?

When reading some literatures on topological insulators, I've seen authors taking Brillouin zone(BZ) to be a sphere sometimes, especially when it comes to strong topological insulators. Also I've seen ...
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317 views

Exact diagonalization by Bogoliubov transformation

I am developing a model of multiple gaps in a square lattice. I simplified the associated Hamiltonian to make it quadratic. In this approximation it is given by, $$ H = \begin{pmatrix} \xi_\mathbf{k} ...
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126 views

Finding difficulties in taking continuum limit in nonlinear sigma model

I am learning nonlinear sigma model from Assa Auerbach's book "Interacting Electrons and Quantum Magnetism" and getting some difficulties in taking continuum limit. I am following chapter 12: The ...
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344 views

Do EM waves transmit spin polarization?

Suppose you have a normal dipole antennae (transmitter and receiver) . Spin polarized current (as opposed to normal current) is sent into the transmitter, it emits an EM wave and the Receiver receives ...
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420 views

How can one localize the massless fermions in Dirac materials?

I noticed that finite electric potential cannot localize the low energy excitations in a graphene sheet. Is it possible to localize the massless fermions in the surface band of topological insulators ...
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47 views

Mean-field theory : variational approach versus self-consistency

I have a general question concerning mean-field approaches for condensed matter classical of quantum statistical mechanic systems. Does determining the mean-field by a variational approach always ...
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230 views

Significance of Dirac cones in condensed matter physics

In condensed matter physics, Dirac cones can be found in graphene, topological insulators, cuprates, and iron-pnictides. This means that electrons behave as massless particles near the Dirac points. ...
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169 views

What happens to a Luttinger liquid under time reversal?

Suppose you a have an ordinary Luttinger liquid with $$ H = \int dx \sum _{\eta= \pm 1 , \sigma =\uparrow,\downarrow } \psi^\dagger_{\eta, \sigma} (x) (-i v \eta \partial _x) \psi _{\eta,\sigma} (x). ...
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47 views

Why is the Hubbard model written down so late?

It is just the tight binding model plus on-site interaction. What prevented people from arriving at the Hubbard model?
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28 views

How to distinguish Bose glass and superfluid phases in a harmonic trap?

In mean-field study of Bose-Hubbard model in an optical lattice, what parameter can be calculated to distinguish Bose glass and superfluid in a harmonic trap?
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114 views

Finding the ground state of the toric code Hamiltonian

How do I write by proof, the ground state of the toric code (by Kitaev) Hamiltonian $ H=-\sum_{v}A(v)-\sum_{p}B(p) $ where $A(v)=\sigma_{v,1}^{x}\sigma_{v,2}^{x}\sigma_{v,3}^{x}\sigma_{v,4}^{x}$ and ...
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105 views

Confusion regarding field operators

Second quantisation of the scalar field leads to an algebra of quantum field operators $$ [\phi(x),\phi(y)] = 0, \ \ [\pi(x), \pi(y)] = 0, \ \ [\phi(x),\pi(y)] = i\hbar \delta(x-y). $$ Where the field ...
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70 views

Third-order topological quantum phase transition in p+ip superfluid

A two-dimensional spinless non-relativistic p+ip superfluid undergoes a quantum phase transition between the BCS (weakly-coupled) and BEC (strongly-coupled) regimes. This transition is driven by ...
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344 views

Toward the establishment of non-equilibrium (quasi-equilibrium) magnon BEC theory

In 2006, Demokritov et al have reported that they have achieved the observation of quasi-equilibrium magnon Bose-Einstein condensation (BEC) in YIG at finite (room) temperature by using the method ...
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238 views

What is the difference between spin glass and spin liquid?

What is the difference between spin glass and spin liquid? Do they both originate from frustration?
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386 views

Why do Fermi liquids have T^2 resistivity?

I have often read that metals that are Fermi liquids should have a resistivity that varies with temperature like $\rho(T) = \rho(0) + a T^2 $. I guess the $T^2$ part is the resistance due to ...
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118 views
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29 views

Spin wave theory for 1D spin systems

In general, when one performs spin-wave theory, he has to assume some kind of long-range ordered state and perform spin-wave theory (using for instance Holstein-Primakoff bosons) around that state. ...
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38 views

What kind of free energy do we use for a superconductor in a magnetic field?

My reasoning is as follows (using Gaussian units): Start from the second law: $$dU=TdS+dW,$$ where $dW$ is the work done by the magnetic field. To derive $dW$, we consider a solenoid with current ...
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46 views

Question about bosonization method

I have a question about bosonization method used in 1D system. Generally the bosonized field is assume to the following form \begin{equation} \psi = e^{i\phi}, \quad \phi = \phi^\dagger ...
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59 views

Neel order and O(3) model

The coarse grained fluctuations of the Neel order parameter in the half integer spin anti-ferromagnetic Heisenberg model is described by the O(3) non-linear sigma model with a strange berry phase ...
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59 views

Topolgical insulators order parameter

For topological insulators Is there any way to define order parameter for topological phase transitions?
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62 views

What does “optical conductivity” mean?

Does it just mean "AC electric conductivity"? If so, why have a special name for it, and why mention optical specifically? The wikipedia page on it is very sparse. This (warning, PDF) document just ...
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117 views

Why is there a Majorana zero mode in the $\pi$ flux core of the p+ip superconductor?

In this review paper (http://arxiv.org/pdf/1202.1293.pdf), the author shows that threading a $\pi$ flux through a 2D $p_x+ip_y$ superconductor will trap a Majorana zero mode at the flux center. The ...
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157 views

Is non-relativistic quantum field theory equivalent with quantum mechanics?

Related post Can we "trivialize" the equivalence between canonical quantization of fields and second quantization of particles? Some books of many-body physics, e.g. A.L.Fetter and ...
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65 views

1+1D Bosonization on a line segment or a compact ring

I have been informed that 1+1D Bosonization/Fermionization on a line segment or 1+1D Bosonization/Fermionization a compact ring are different - Although I know that Bosonization can rewrite fermions ...
3
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377 views

Numerical problem in solving the Bogoliubov de Gennes equations- methods to solve?

I am trying to solve an assignment on solving the Bogoliubov de Gennes equations self-consistently in Matlab. BdG equations in 1-Dimension are as follows:- $$\left(\begin{array}{cc} ...
3
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126 views

Does the projected spin state of the $d+id$ mean-field Hamiltonian on a triangular lattice has time-reversal(TR) symmetry?

Consider the following $d+id$ mean-field Hamiltonian for a spin-1/2 model on a triangular lattice $$H=\sum_{<ij>}(\psi_i^\dagger\chi_{ij}\psi_j+H.c.)$$, with $\chi_{ij}=\begin{pmatrix} 0 & ...
3
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85 views

Zumino's consistent and covariant anomalies - applied to quantum hall?

What is the `physical' meaning of consistent anomalies and covariant anomalies? Perhaps a good Reference is: Consistent and covariant anomalies in gauge and gravitational theories - William A. ...
3
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73 views

What does the term 'a uniform RVB spin-liquid state' mean?

I encountered this term a uniform RVB spin-liquid state in some articles, for example, see the paragraph under Eq.(29) on page 9 in this paper. What does the word 'uniform ' mean? Simply from the ...
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51 views

Two Photon Absorption dependence on Semiconductor Band Gap

It's well known that Two Photon Absorption coefficient is scaling with $E_g^{-3}$. Does anyone know what is the physical reason for this scaling? What is the physical theory behind this mathematics?
3
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183 views

Some ambiguous points on Spontaneous Symmetry Breaking (SSB)?

Almost in every textbook of condensed matter physics, the standard description of SSB could be formulated as follows: Consider the lattice Heisenberg model in an external magnetic field ...
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262 views

Definition of 'Majorana Number' in the Kitaev Chain

I have some questions about the Kitaev toy model for Majorana fermions (arXiv:cond-mat/0010440). First of all, his proof for the definition of the 'Majorana number' is not so clear to me. $$P(H(L_{1} ...
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139 views

Quantum Hall Effect and Edge States

In quantum hall effect we measure the hall conductance (in transverse direction) which is quantized. My question how do they take care of the edge states that are in the longitudinal side?
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70 views

Is there a critical order of the Abelian gauge theory in (2+1)D

In (2+1)D spacetime, it is known that the $U(1)$ gauge theory is always confined (according to Polyakov), while the $\mathbb{Z}_2$ gauge theory can support a deconfined phase. Now consider a generic ...
3
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81 views

Two-fluid description of superfluidity

I'm trying to teach myself about superfluidity and I'm slightly confused on the ''two-fluid'' description. From what I understand, the superfluid is considered to be a mixture of two fluids, a ...
3
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446 views

Goldstone modes and Heisenberg model

The ideia is to show that, because of Goldstone modes, 2d systems are quite different from 3d ones. So, considering the Heisenberg model, I'll post here what I'm asked to and my current thoughts on ...
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104 views

Qualitative argument to determine energy of defects

In a book of "LES HOUCHES - Critical Phenomena, Random systems, Gauge theories" the author Frolich says that: 2D In two dimensions, the mean energy of an isolated point defect in a square area of ...
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122 views

Nonlinear anomalous Hall effect

Has there been any research on anomalous Hall effect which would observe or predict a non-constant dependence of the AHE conductivity on the applied electric field?
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26 views

Is that possible to derive Landau-Fermi liquid theory from microscopic equation?

The question arised from reading Wen's book "Quantum Field Theory of Many-body Systems (Oxford 2004)" p204 To appreciate the brilliance of Landau-Fermi liquid theory, let us look at the ...
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48 views

Proximity effect and integrating out the quasiparticle degrees of freedom

I am reading at the moment the paper http://arxiv.org/abs/1401.5203 and try to reproduce the results. One result is the proximity correction $S_{\Sigma}$ to the system $$ e^{-S_{\Sigma}} ...
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27 views

Chern bands and HEP Lattice Fermions: the emergence and the exact map

Chern bands or Chern insulators in 2 spatial dimensional(2D) are a way to construct the bulk insulating gap, but with edge or surfaces with gapless fermions. Such gapless fermions are emergent, and ...
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54 views

Strong interacting v.s. Strong Coupling v.s. Strong Correlated

One of the active research areas in present is Strong interacting, Strong Coupling, Strong Correlated regime of the phases of matters. It seems to me that some physicists in the fields often mix the ...
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84 views

How to understand the equivalence between Andreev reflection and Cooper pair injection?

It is well know that Andreev reflection dominates the subgap transport at the normal metal-superconductor interface. An incident electron can be reflected as a hole in the Nambu space, which ...