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

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Existence of effective Hamiltonian for variational ansatz

I recently saw on Wikipedia that in perturbation theory one can define in a systematic way effective Hamiltonian $\hat{H}_{\rm eff}$ that produces the same kind of states and energies as if one ...
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26 views

Homotopy Theory for Topological Insulators

I'm trying to understand topological insulators in terms of homotopy invariants. I understand that in 2 spatial dimensions, we have Chern insulators since $$\pi_2(S^2) = \mathbb{Z}$$ One subtlety that ...
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1answer
21 views

Exact expression for the ground state energy in the 1D Bose-Hubbard model

I heard that Bose-Hubbard model is exactly solvable in 1D. What is then expression for the ground state energy $E_{0}(N, M, ...)$ as a function of total number of particles $N$, number of lattice ...
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22 views

Quantum Confinement in Quantum Dots

I have seen it referenced in several places that an electron will behave classically in a bulk material but as the dimension of the material in which the electron exists is limited below the electron'...
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1answer
61 views

Proper definition of the Wannier function

I am studying the construction of the Wannier functions for 1D system with periodic boundary conditions and my reasoning seems to be a little bit different from what I can find in textbooks. First ...
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24 views

Sublattice symmetry vs Particle hole symmetry

Sublattice symmetry and particle hole symmetry generally constrain a system's energy spectrum to be symmetric with respect to fermi level. My understanding is that they are both represented by an ...
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1answer
47 views

Majorana fermion [on hold]

I know that in condensed matter physics Majorana fermion is neutral and one fermion can be split into two Majorana fermions and vise versa. My question is charge. Two neutral particles can merge into ...
2
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1answer
31 views

Switching Parity in a Superconductor

I've got a pretty simple question that's been bothering me for a while. This is the issue. Suppose we have a superconductor with phase $\phi$, and we change this to $\phi+2\pi$. One would think that ...
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45 views

Why are topological phases described by modular tensor categories?

After some reading, I have an inuitive idea what topological phases of matter are. But where is the connection to modular tensor categories? Is there fundamental literature where this is covered? ...
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29 views

Renormalization Group in Condensed Matter [closed]

Are RG calculations done only in the vicinity of a phase transitions in cond-matt?
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110 views

How does superfluids and Bose-Einstein Condensates form?

Superfluids or Bose-Einstein Condensates can form from bosonic particles (such as the integer spin 0 $^4\mathrm{He}$) at low temperatures near absolute zero when all the bosonic particles in it start ...
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1answer
41 views

Can superfluids pass through ordinary baryonic matter?

Since superfluids consists of integer spin bosons or effective bosonic Cooper-paired fermions, Pauli Exclusion Principle does not apply to them. They can thus occupy the same quantum state as any ...
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36 views

Systems with extensive ground state degeneracy

This is sort of a follow up to this question: What does it mean for a Hamiltonian or system to be gapped or gapless? There it is stated in one of the answers that a system is gapped if it fulfills ...
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33 views

What is the recursive relation for three-particle Green's functions?

In condensed matter physics, one often choose to study the many-body Green's functions (GF) with the diagram (perturbation) expansion technique. In what follows only two-body interaction is concerned. ...
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17 views

Ionic polarisation: wave-vector of photon ~ 0

While discussing ionic polarization due to electromagnetic waves we discuss interaction of photons and ions of crystal. Now, the next step is to take conservation of momentum under consideration. ...
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1answer
53 views

Examples of short-range correlated gapless systems

I thought this must have been asked before, but couldn't find it through search. It was proved by Hastings and Koma in arXiv:math-ph/0507008, given a Hamiltonian satisfying certain locality ...
6
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1answer
75 views

Does Bose-Einstein Condensate other than liquid helium exist?

I have basic understanding of BEC - if you can call it understanding -, and I did a lot of reading to get it, but I never came across any examples other than liquid helium. Is it theoretically ...
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2answers
71 views

Bogoliubov transformation is not unitary transformation, correct?

To diagonalize quadratic term in the antiferromagnet Heisenberg model, we may introduce the Bogoliubov transformation:$a_k=u_k\alpha_k+v_k\beta_k^\dagger$, $b_k^\dagger=v_k\alpha_k+u_k\beta_k^\...
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1answer
31 views

Quantum ising/heisenberg model, states representation

I am working with a hamiltonian which looks like this (Heisenberg model) I have made a program which computes this hamiltonian using Pauli matrices (spin 1/2). My working space is then the tensor ...
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1answer
48 views

Simple analytic examples of MERA

I want to understand Multi-scale Entanglement Renormalization Ansatz (MERA) with very elementary examples. So far I could find references which are mostly based on numerics. It would be a great help ...
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34 views

Stoner-Wohlfarth model for ferromagnetism

I'm studing the Stoner-Wohlfarth model for ferromagnatism on the book Ibach-Luth Solid state physics. During the derivation of the Stoner criterion I found this passage (8.43) not so clear for me: ...
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39 views

What is the current status of the field of quasicrystal?

So this is a soft question. I am just wondering what is the current status of the field of quasicrystals? Does this kind of material have any real life application? Is it a possible playground for ...
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10 views

Quadrupolar interaction

In http://journals.aps.org/prb/pdf/10.1103/PhysRevB.64.195109 Eq.(4), why does the Fourier transform of the quadrupolar interaction function takes the form \begin{equation} F(\mathbf{q})=\frac{F_2}{1+...
4
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1answer
43 views

Something about non BCS pairing

When I have read about literatures, the non-BCS type superconductor always involve some kind of pairing which the energy gap $\Delta$ is not a constant but a function of momentum $k$: $\Delta=\Delta(k)...
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31 views

Projected band structure plot - orbital characteristics plotted vs the K values?

I'm not understanding what is it that I have to plot for obtaining the orbital characteristics of a band in the band structure diagram. Usually we plot the energy eigenvalues for a given k point. ...
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1answer
38 views

Converting the Hamiltonian for the tight binding model in silicene into $k$ space

I am trying to convert the Hamiltonian from the paper "A topological insulator and helical zero mode in silicene under an inhomogeneous electric field" (also on arXiv) into $k$ space. $$H = -t\sum_{\...
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65 views

Definition of a gapless spin liquid

I understand the definition of a gapped spin liquid: it's a gapped, topologically ordered spin state - i.e. there does not exist a local unitary transformation that takes it to a product state in ...
4
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55 views

Are second-order phase transitions always scale/Lorentz invariant?

I know that both scale invariance and Lorentz invariance typically emerge at second-order phase transitions, but is there a proof or a counterexample? (I know that it's believed that any theory that ...
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26 views

Distinguishing Insulator, Metal, Superconductor by a flux insertion argument

I have the following argument to distinguish Insulator, Metal and Superconductor. For simplicity let's consider electrons on a circle and thread one quantum of flux (e$\Phi_0 = 2\pi$) through it (or ...
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1answer
30 views

Derivation of a commutator in the Luttinger liquid theory

I am reading the book by Nagaosa: quantum field theory in strongly correlated electronic systems. In chapter 2, he introduces the Luttinger liquid theory. I find some difficulty to reproduce his ...
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113 views

Computational scaling of quantum and classical Monte Carlo algorithms

How does the computational complexity of finding an equilibrium thermal state for a given Hamiltonian at a given temperature scale with system size under classical and quantum Monte Carlo? I know ...
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25 views

Chiral spin liquid flux states on the Kagome lattice

Short version: Is it possible to arrange the fluxes for the Kagomé lattice with triangle flux $\phi_\triangle=\frac{\pi}2$ and hexagon flux $\phi_{hex}=0$ using a single unit cell? Longer version: I ...
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2answers
41 views

What is the difference between crystals and solid? [closed]

In condensed matter physics, what are the differences between crystals.
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21 views

Why Weyl fermion in Weyl semimetals(WSM) have high mobility only at low temperature?

I read several papers reporting high Weyl fermion with very high mobility in WSMs such as TaAs, NbAs, WTe2 and so on. However, this high mobility looks like (=Weyl fermion) always appears at only low ...
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160 views

Relationship between crystal momentum and true momentum

Most textbooks make it clearly that crystal momentum is not true momentum. However, in a lot of literature, crystal momentum is treated as true momentum. Here's two examples: Rashba spin splitting. ...
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71 views

How can one intuitively understand formulas of the form $χ\sim\sum_{\bf k}{f_{\bf k}-f_{\bf k+q}\over ε_{\bf k+q}-ε_{\bf k}}$?

When calculating various susceptibilities, we get below formula again and again. $$\chi( {\bf q},0) \sim \sum\limits_{\bf{k}} {\frac{{{f_{\bf{k}}} - {f_{{\bf{k}} + {\bf{q}}}}}}{{{\varepsilon _{{\bf{k}}...
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38 views

Decomposition of the Time-Evolution Operator: Translationally Invariant MPO

Hello everyone myself Sudipto. Currently I'm learning the matrix product state technique in order to simulate 1d spin system and study different properties of the system form quantum information ...
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3answers
51 views

Why alloy have more resistance?

Is there any simple way to understand why alloy have more resistance than metals? My teacher ask this, I answer that, there might be more free electrons in metals than an alloy, but she said you are ...
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1answer
50 views

Vacuum persistance amplitude

E. Fradkin's Field Theories in Condensed Matter Physics formulas 3.57 and 3.58: I feel really sad about it, but all my tries of getting from formula $$ Z = \operatorname{tr} \hat{T} \prod_{j=1}^{...
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46 views

Is there a block spin renormalization group scheme that preserves Kramers-Wannier duality?

Block spin renormalization group (RG) (or real space RG) is an approach to studying statistical mechanics models of spins on the lattice. In particular, I am interested in the 2D square lattice model ...
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2answers
73 views

How do signals go through solid objects? [closed]

So many types of signals pass, or seem to pass I don't know, through solid objects. How do they do this?
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39 views

RPA Charge Instability in One Dimensional Electronic Systems

As we know, no long range order in a one dimensional electron system is expected due to quantum fluctuation. A typical 'phase diagram' for a system with short-range interactions is shown on page 69 of ...
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11 views

Orthogonality condition between core and valence states (pseudopotentials)

In the paper "Pseudopotential methods in condensed matter applications" by W. E. Pickett the author comments the following in the introduction section (Page 4, 1st paragraph - introduction) "Although ...
2
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23 views

Deriving Reciprocal Lattice Definition

The derivation of reciprocal lattice vectors in terms of the direct space lattice vectors starts by applying expanding a translationally invariant lattice function $f(\bf{R_k}+r)$ in plane waves $f_k ...
2
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45 views

Bosonization for unequal left/right Fermi velocities

The standard exposition of bosonization/Luttinger liquid theory in textbooks treats the case that left and right channels share the same absolute value of Fermi velocity. Is it possible to relax this ...
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15 views

Will two Weyl points which belong to a Weyl pair be transformed to each other by inversion symmetry?

In solid state system, A Weyl pair can be obtained by splitting a Dirac node when time reversal symmetry is broken and inversion symmetry is reserved. My question is that Whether the inversion ...
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231 views

Intuition behind transforming a Hamiltonian expressed in momentum representation in eigenbasis [closed]

This question is a supplement to a previous question on the same paper. In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve ...
2
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1answer
46 views

Is edge states of topological insulators superconducting?

I am told edge states of topological insulators are free from back scattering. Does this mean topological insulators have no resistance if only edge states are taken into account?
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44 views

Connection between fractional charge and Schrodinger's cat

In the FQHE, it is said that one electron splits into three 1/3-charged entities. Is it like the Schrodinger cat?
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Density of States for a separable hamiltonian

There are $N$ non interacting electrons in a potential well: \begin{align} H&= -{1 \over 2 } \nabla^2 + U(x,y,z) \\ U(x,y,z)&={1\over2}\omega^2z^2 \; \mbox{for} \; (x,y) \in [0,L]\times [0,L]; ...