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

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Kane and Mele's argument on the existence of edge states in quantum spin Hall effect of graphene

Borrowing from Laughlin's argument on quantum Hall effect, Kane and Mele argued why there must be edge states in graphene with spin-orbit coupling in one paragraph, which is above the one with ...
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20 views

Generalization of a spin-glass order parameter definition

I am going through the paper, Solving the graph-isomorphism problem with a quantum annealer, by Hen et. al. Equation 4 on the second page gives the definition of the spin-glass order parameter as ...
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71 views

Difference of the O(N) Non-linear Sigma model and SO(N) Non-linearSigma model

The Hamiltonian \begin{equation} H=J\sum_{i,j}\vec{n}_i\cdot\vec{n}_j \end{equation} is invariant under a global rotation $\vec{n}_i\rightarrow R\vec{n}_i$, where $\vec{n}$ is a $N$ component rotor ...
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274 views

Naive questions on Goldstone modes and a possible duality relation?

For example, let's consider a 1D spin-1/2 ferromagnetic (FM) Heisenberg chain $H=-J\sum_{i=1}^{N}\mathbf{S}_i\cdot\mathbf{S}_{i+1}$ with periodic boundary conditions. Now we want to study its low ...
2
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1answer
69 views

Hamiltonian for the Periodic Kitaev Model

The Hamiltonian for a system of spinless fermions on a 1D chain (with chemical potential $\mu=0$) is given by $$ H=-\sum_j\left( c^\dagger_{j+1} c_j+h.c.\right)+\Delta \sum_j \left( ...
5
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1answer
186 views

How to derive electron number equation of Bogoliubov Hamiltonian using thermodynamic relations.

My question arise from this article: Edge superconducting correlation in the attractive-U Kane-Mele-Hubbard model. I will describe my question in detail so that you might not need to look into that ...
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27 views

For the gapped phase of Kitaev model, where does the first excited state reside in, the zero-flux sector or not?

As we know, there are both gapless and gapped ground states of the Kitaev model, and let's fix the couplings $J_x,J_y,J_z$ such that the model being in the gapped phase. My question is, does the first ...
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108 views

Two-Dimensional Tight-Binding Dispersion Relation

As in my last post, I am doing out a calculation in Giamarchi's Many-Body text: http://dpmc.unige.ch/gr_giamarchi/Solides/Files/many-body.pdf. This time, I am going through the derivation of the ...
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54 views

What is the minimal symmetry required for a spin Hamiltonian to describe a spin-liquid ground state?

Let's restrict to the case of spin-1/2 system. As we know, a spin-liquid (SL) state is the ground state of a lattice spin Hamiltonian with no spontaneous broken symmetries (sometime it may ...
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1answer
129 views

Solving the BCS Hamiltonian via the Bogoliubov Transformation

I was doing a calculation in Giamarchi's Introduction to Many Body Physics, chapter 3, on BCS theory and second quantization, and ran into some confusion with the BCS Hamiltonian. The pdf is here for ...
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66 views

Number of Goldstone bosons in paramagnetic-to-ferromagnetic phase transitions

In paramagnetic-to-ferromagnetic phase transitions, the symmetry spontaneously breaks down from SO(3) to the subgroup SO(2) below $T_\text{crit}$. This implies that there should be two Goldstone modes ...
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1answer
44 views

Locality in Condensed Matter Lattice Model

What is a proper definition of locality in condensed matter lattice model? I emphasize "condensed matter" because there is no Lorentz symmetry or "speed of light". I think it is quite important ...
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175 views

Does electron-electron scattering contribute to resistivity?

Electron-phonon and electron-defect scattering clearly contributes to resistance, but pure electron-electron scattering conserves the total momentum (and energy) of all the electrons. Then, how is it ...
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0answers
28 views

In k$\cdot$p theory, how does one calculate the bulk inversion asymmetry coefficients given in table 6.3 in Winkler?

In k$\cdot$p theory, how does one calculate the bulk inversion asymmetry coefficients given in table 6.3 in Winkler? Winkler's book on spin-orbit coupling effects is available free online. In ...
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25 views

Phase coherence and interference effects in Anderson localization

Anderson localization results from wave interference of the between multiple-scattering paths from random impurities, yielding wavefunctions with exponentially decaying tails and absence of diffusion. ...
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65 views

Higgs Boson and its relation to the vacuum

The Higgs boson and the electroweak theory used symmetry breaking from condensed matter physics as its inspiration. The BCS theory of superconductivity is one such condensed matter symmetry breaking ...
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90 views

Gutzwiller mean-field method in Bose Hubbard model

Gutzwiller mean-felid method is an efficient way to study Bose-Hubabrd model in optical lattice with a harmonic trap. Gutzwiller method assumes there is no spatial correlation within the trap, so ...
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175 views

Why are there gapless excitations in the anti-ferromagnetic Heisenberg model while the true ground state is a singlet?

The true ground state of the anti ferromagnetic quantum Heisenberg Model (nearest neighbor only)is known to be a singlet (I think this is Liebs theorem.) Since a singlet is invariant under rotations, ...
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84 views

Is linear momentum conserved in a system with open boundary conditions?

In a one dimensional lattice system with periodic boundary conditions, in which the last and the first site of the lattice are the same site, momentum is conserved modulo a vector of the reciprocal ...
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1answer
109 views

A formula in Sung-Sik Lee's paper

I want to ask if anyone has gone through the derivation of the second equality in the following formula which comes from http://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.165102.
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24 views

Superfluid momentum distribution

Bosons confined in a optical lattice under some conditions can enter a superfluid phase. Momentum distribution can be measured using time of flight method. But why is there a sharp peak in momentum ...
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58 views

Question about Bose-Hubbard Model

By using an optical lattice, how can one change the interaction term $U$? And how is the superfluid phase achieved in the hard-core boson regime? Why are these phases identified as superfluid or mott ...
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26 views

Order of Monte Carlo integration and frequency summation

I am currently trying to calculate an integration formula of a linear response function by Monte Carlo method. It is a multiple integration over three 3D vectors, i.e., nine dimensions in all. And ...
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2answers
239 views

Why are Cooper pairs formed by electrons of opposite momentum and spin?

I understand that Cooper pair in low-temperature superconductivity are formed by electron-phonon interaction. Normally one then assumes that electrons of opposite momentum and spin are paired. This is ...
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317 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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57 views

Should Brillouin zone be a continuous object rather than a discrete one in the thermodynamic limit?

For example, just consider a 1D atom chain with $N$ sites and lattice constant $a=2\pi$, under periodic boundary conditions, the crystal momentum reads as $k=\frac{n}{N}\frac{2\pi}{a}=\frac{n}{N}$, ...
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43 views

1D Hubbard model in the negative U limit

In the 1D Hubbard model at half-filling, is the ground state considered as a charge-density wave (CDW) state in the very negative U limit? Is there a long range order exist in this case? Is a CDW ...
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2answers
105 views

Question about Landau's phase transition theory

I have a question about Landau's theory of quantum phase transition. In his model, the free energy is assumed to be \begin{equation} F = f_0 + \alpha (T-T_c) \Delta^2 + \beta \Delta^4 ...
2
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1answer
51 views

How does band gap vary with the cell volume?

How does band gap vary with the cell volume? is there a relation? If the volume is compressed, the interaction between atoms would be more, therefore the perturbation is higher hence the splitting ...
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28 views

Snowmaking in the tropics - an estimate of water evaporation

If I set up a snowmaker in the tropics and sprayed water with it how much water would I evaporate? How would I calculate?
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1answer
40 views

Difference between non-collinear systems and paramagnetic ones?

Non-collinear magnetism and paramagnetism, are they the same thing?
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1answer
125 views

Anyons only in 2+1 spacetime dimensions - better explanation

Regrading why anyons exist only in 2+1 spacetime dimensions (which have an arbitrary phase on exchange), I read the reason that the paths for exchange in 3D are deformable into each other while in ...
2
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1answer
92 views

How to calculate energy in two-band Hubbard model

It might be a very easy question for you, but I am confused and I need helps. In the simplest Hubbard model at one-dimensional lattice, I ignore the $U$ term and only remain the hopping term. ...
2
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1answer
111 views

Why do He-3 atoms repel each other much more strongly than electrons?

Is there a simple answer to this question ? see last line of this paragraph http://en.wikipedia.org/wiki/Fermionic_condensate#Fermionic_superfluids
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1answer
153 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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1answer
60 views

'Pseudo-Relativistic' behavior in Graphene

I've read that electrons in Graphene behave 'pseudo-relativistically'; what does this mean? how do they behave differently from electrons in other materials?
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1answer
74 views

What is $\epsilon_\infty$ in this equation and why can it be neglected in the IR?

I'm reading this paper (warning, PDF) and they mention that the complex permittivity $\epsilon$ and complex conductivity $\sigma$ are related through the equation $$\epsilon - \epsilon_\infty = (4\pi ...
2
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1answer
92 views

What happens to the free energy of the two-dimensional ising model with vortices?

The classical 2d Ising model has a Hamiltonian of the form: \begin{equation} H = -\sum_{m,n = 0}^{M,N} J_1 x_{m,n}x_{m+1,n} + J_2 x_{m,n}x_{m,n+1} \end{equation} The partition function for the model ...
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1answer
121 views

Functional field integral in condensed matter field theory (Altland)

This is the action for the 1+1 dimensional interacting electron system; $$S_{cl}[\theta , \phi]= \frac{1}{2\pi} \int dxd\tau \left(g^{-1}v(\partial_x \theta)^2 + gv(\partial_x \phi)^2 + ...
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69 views

Interacting fermionic SPT phases in 2d with time-reversal symmetry

Interacting fermionic SPT phases in 1d and 3d with $\mathbb{Z}_2^T$ symmetry are classified by $\mathbb{Z}_8$ and $\mathbb{Z}_{16}$ respectively, as shown in the paper by Fidkowski and Kitaev ...
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2answers
503 views

Why can, or can not, a perfectly incompressible fluid exist?

Water is normally assumed to be an incompressible fluid - for example in the context of calculations involving water pressure. I wondered whether that is strictly true, or an approximation? Later I ...
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74 views

Questions on degenerate ground states and the thermodynamic limit?

For example, let's consider a $N$ spin-1/2 system on a lattice described by the Hamiltonian $H$. My questions are: (1) If $H$ has either global $SU(2)$ spin-rotation symmetry or time-reversal ...
5
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1answer
155 views

Will all physical quantities unchanged by this transformation?

I am reading an article about Bloch-Floquet state. My questions is in Part II.B and Appendix A of this paper, I will describe them below. The original Schordinger equation we consider is: ...
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146 views

Jordan Wigner Transformation in 1d Majorana chain

So, I was reading the paper by Fidkowski and Kitaev on 1d fermionic phase http://arxiv.org/abs/1008.4138. It explains the classification of 1d fermionic SPT phases with $\mathbb{Z}_2^T$ symmetry for ...
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0answers
52 views

What is a “charged order parameter”?

In condensed matter physics, especially in the context of superconductors, if an author uses the phrase "charged order parameter", what does it refer to? Since the superconductor has a close relation ...
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1answer
77 views

Numerical Tools to find Braiding Statistics of Quasiparticles

While certain classes of systems that exhibit topological order can be solved exactly (such as the Toric Code, Abelian FQH Edges, etc.) there also exist systems (think of perturbed versions of the ...
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1answer
48 views

Wannier functions on a ring

Let's say I have a single particle hamiltonian in a periodic potential, for example a 1D lattice such that: $$H = -\frac{\partial_x^2}{2m} + V(x) $$ with $ V(x+a) = V(x)$ where $a$ is the lattice ...
5
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1answer
224 views

Degenerate perturbation theory applied to topological degeneracy?

Consider a quantum system described by a gapped Hamiltonian $H_0$ with degenerate ground states (GS), adding a perturbation term $V$ to $H_0$, then the low-energy physics can be described by an ...
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2answers
97 views

Free electron gas in two dimensions

Can someone give a qualitative description on why the density of states for a two dimensional free electron gas is independent of energy while it is not in one and three dimensions? In one dimension ...
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52 views

Approximation of skeleton diagrams

I'm studying the diagrammatics for a Bose system (in the superfluid phase) developed by Gavoret and Nozieres (Annals of Physics 28 349 (1964)). In this paper, they show how to solve the problem using ...