Questions tagged [strong-correlated]

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What's the difference of flux tube and vortex in FQHE (especially in Jain wavefuntion)

In the book Composite Fermion by Jainendra K.Jain, he mentioned the motivation of Jain wavefunction: attach flux tube of 2p flux quantum to fermions to form composite fermions. Naively, this is done ...
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3 votes
2 answers
68 views

Is a highly entangled quantum system synonymous with a strongly correlated system?

Is a highly entangled quantum system synonymous with a strongly correlated system? From wikipedia a key characteristic of a strongly correlated system is that "the behavior of their electrons or ...
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Dynamical Mean Field Theory (DMFT) does not take into account spacial correlations?

It is often said that the Dynamical Mean Field Theory (DMFT) does not take into account spacial correlations. What does this mean in layman terms? Does that mean that we assume: $$ \langle n_i n_j \...
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3 votes
1 answer
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Periodic Anderson model vs Anderson impurity model?

What is the difference between these two models? I would appreciate if the answer could provide me with some useful references from which I can learn these models. I saw that periodic Anderson model ...
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What are single particle states used in occupation number representation for correlated systems?

As I understand, the many-particle states are formed from the basis states of the single-particle vector spaces; occupation numbers then represent the number of particles in corresponding single-...
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Mapping between spinful fermions and spineless fermions

I encounter a problem in understanding the mapping between spinful and spineless fermions. This method is discussed on TenPy. Suppose our system is described by 1D spinful fermion Hubbard Hamiltonian. ...
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1 answer
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$\mathbb{Z}_2$ gauge theory and disorder

I am confused about basics of $\mathbb{Z}_2$ (and likely other) gauge theories and plain disorder. Let $$H=H_F + h\,H_{EM}$$ $$H_F = -t\sum_l (c^\dagger_l \sigma^z_{l,l+1} c_{l+1} + h.c.)$$ be (the '...
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Do correlations in local quantum spin systems always decay exponentially or algebraically?

Consider translation-invariant quantum spin systems, that is qu-d-its on a lattice with a geometrically local Hamiltonian. Usually, such models are either gapped (in an ordered/disordered phase) or ...
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Does Symmetry breaking happen in $SU(N)$-Anderson model in large-$N$ limit?

Consider the following $SU(N)$-Anderson model, $$H = \epsilon_{}^{}\sum_{\sigma=1}^{N} c_{\sigma}^{\dagger}c_{\sigma}^{}+\sum_{\sigma=1}^{N}\sum_{k}^{}\epsilon_{k}^{}d_{k\sigma}^{\dagger}d_{k \sigma}^{...
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Asymptotic states in strongly-coupled QFTs

In QFT the asymptotic states play a very important role, as they are the basis on which we decompose our in-states and out-states when we calculate correlation functions. However, I have not been ...
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Interpretation of occupation numbers and creation-annihilation operators in strongly correlated systems

I hope I am not asking anything stupid, but I am having a hard time interpreting some (seemingly simple) results. The simplest approximate form of an $N$-electron wave function (w.f.) is a Slater-...
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Paths for Learning Keldysh Field Theory [duplicate]

I am an physics undergrad in my pre-final year. Recently, I tried learning some QFT (from the likes of Peskin and Schroeder’s 1st 4 chapters, David tong etc.) and got interested in it’s working in a ...
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1 answer
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What is the physical meaning of the Kondo Temperature?

From my understanding, in a Kondo lattice, the Kondo temperature is where the resistivity dramatically drops. I've also read that the Kondo temperature is the only real "scale" in the physics, with ...
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What is the QM equivalent of induction?

And regarding electron correlations, reciprocally what QM ones are strictly due to classical induction and near field effects? Edit: thanks to whoever thinks necessary to downvote questions without ...
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1 answer
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Momentum Space Representation of the Tight Binding Hamiltonian

I am trying to represent the tight-binding Hamiltonian \begin{equation} \hat{H}_{TB} = \sum_{\sigma} \sum_{\alpha,\beta} \sum_{\mathbf{R}_1,\mathbf{R}_2} t^{\alpha,\beta}_{\mathbf{R}_1,\mathbf{R}_2} \...
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Electron correlation - difference between correlation and dependence

When we talk about electron correlation in condensed matter physics or chemical physics, we usually refer to the fact that the pair-density $$ P(r,r') = N(N-1) \int |\psi(r,r',r_3,...,r_N)|^2 \; \...
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Finite temperature QFT: Can vertex correction function/ initial correlations induce short-time tunneling?

The collision term in the Kadanoff-Baym equation has the structure $I(\tau_1,\tau_2) = \int_C d \tau'\Sigma(\tau_1,\tau') G(\tau',\tau_2)$ where the contour $C$ is along the time-Forward $C_+$, time-...
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Destruction of Mott phase by a external magnetic field

I want to ask the underlying reason for the destruction of Mott insulating phase by an external magnetic field. I know that for a normal band insulator, the transition to a metallic phase can be ...
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33 votes
2 answers
831 views

Can we get complete non-perturbative information of the interacting system by computing perturbation to all orders?

As we know, the perturbative expansion of interacting QFT or QM is not a convergent series but an asymptotic series that is generally divergent. So we can't get arbitrary precision of an interacting ...
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How exact are the Kadanoff-Baym equations?

In a General nonequilibrium Quantum chemical System, the Kadanoff-Baym equations have the form: $(i \partial_t -h_2-\Sigma_{H,2})G_<(1,2) = \delta_C(1, 2) + \int d3 \Sigma (1,3)G_<(3,2)$ where ...
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The link between spin singlet and the emergent (heavy fermion) fermi liquid in Kondo physics

I have been trying to understand the Kondo physics. Based on Anderson model, at low temperature $T<T_\text{K}$, the local spin gets screened by the itinerant electrons with a formation of the spin ...
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1 answer
270 views

Inverse Green's Function identity in derivation of Hedin's equations

I'm trying to work through a derivation of Hedin's Equations in Effect of Interaction on One-Electron States by Hedin and Lundqvist (1969) and I've come across an identity that is given without much ...
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2 votes
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240 views

Insulator behavior of large U limit in Hubbard model

I am now learning the many-body physics and having some questions about the insulator behavior of large $U$ limit for the Hubbard model : \begin{equation} H = -t\sum_{\left\langle {i,j} \right\rangle,...
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When constructing Hamiltonian matrix for many spins, what is the significance of the order of factors in the outer product?

I'm trying to learning the Density Matrix Renomalization Group (DMRG) method from the book "Strongly Correlated Systems: Numerical Methods". For a two-spin system they build a Hamiltonian from the ...
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3 votes
0 answers
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Regard to the technical definition of a Mott insulator

I was reading Chapter 16 of the textbook on advanced solid state physics by Philip Phillips. In this chapter, the physics of Mottness is comprehensively discussed. There is a statement he made on page ...
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What's the relation between SDW/CDW and spinon/holon in the one dimensional repulsive Hubbard model?

As is well known, spin-charge separation occurs in the one dimensional repulsive Hubbard model. This phenomenon can be well understood by the Luttinger liquid theory, where spin density wave(SDW) and ...
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1 answer
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strongly correlated limit of the electron gas

In chapter 7 of "introduction to many-body physics" by Coleman, the author calculated the Hartree-Fock contribution to the energy of the electron gas, following which it is claimed that the most ...
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2 votes
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Question about the derivation from 2d Bose Hubbard to Quantum Rotor model

It is well-known that the Bose-Hubbard model (BH) and Quantum Rotor model (QR) can be mapped to each other under certain constraints (here I'm focusing on the 2d case). I was trying to get this ...
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3 votes
1 answer
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Hubbard-Stratonovich transformation in the operator form

I was reading the Chapter 14 of the textbook by Philip Phillips on Advanced Solid State Physics, when he introduced the mean-field treatment of the quantum rotor model, he used the method first used ...
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2 votes
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The quantum field description of the vortex in the Superconductor-Insulator phase transition

I was reading professor Naoto Nagaosa's book on Quantum Field Theory in Condensed Matter Physics about the problem on universal conductivity. On page 156, he showed a method to obtain the QFT ...
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5 votes
0 answers
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How the understand the idea of spatial dependent Fermi wave vector?

Recently, I have been reading the book by Naoto Nagaosa on Quantum field theory in Strongly Correlated Electronic Systems, but I got a problem in Chapter 3.2. When he discuss the idea of Bosonization ...
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What's the exact definition for strong correlation in condensed matter physics?

Can we judge or define the strong correlation (for electron system) in condensed matter physics just by the competition of kinetic energy and interaction energy term in the total Hamiltonian? I mean ...
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Explain the characteristic features of long range entanglement

The long range entanglement (LRE) can exist in fermi liquids or lattice. The characteristic features of long range order entanglement could be the degeneracy, fractional excitation or the entanglement ...
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4 votes
2 answers
956 views

Keldysh formalism and Kubo formula

I am working on out-of-equilibrium problems of strongly correlated materials, so I am interested in the Keldysh formalism. I just started reading about the subject, and I don't understand quite well ...
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3 votes
1 answer
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Why do people always talk about continuous topological phase transition?

I have a question which puzzles me for a long time. Usually when people talk about topological phase transition, they usually have a gap-closing picture in their mind. Namely, the phase transition ...
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5 votes
0 answers
634 views

Book suggestion. (Strongly correlated electron systems)

Can anyone suggest a good book on strongly correlated electron systems which may be starts off with second quantization, goes through Hubbard model, Mott transition, T-J model etc? I have the book by ...
12 votes
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What is a strongly correlated system (in condensed matter physics)?

I was told that a strongly correlated system is such that Fermi liquid theory fails, or a single-particle picture doesn't work. So, there is no energy band for a strongly correlated system. So, I ...
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4 votes
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how can I understand spin fluctuation in iron based superconductors?

In study of iron based superconductors, one of the starting point is that electrons are weakly interacting(or weakly correlated) such that we can still apply many body perturbation theory(so called ...
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0 votes
2 answers
138 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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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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Effective interaction between electron-magnon in ferromagnetic transition metals

I wonder whether there are classical references on an effective theory of electron-magnon interaction in itinerant ferromagnetic metals?
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Intuitive picture for spin-fluctuations contribution to sign reversal of S+- state

In conventional superconductor, electron-phonon interactions lead to negative paring potential and further s-wave superconducting gap. One mechanism for superconductivity in iron-based ...
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2 votes
1 answer
552 views

many body wavefunction and exchange correlation

Everywhere I ready about HF or DFT the term exchange correlation functional comes up. I have a couple of fundamental questions about these: 1) Books say that the correlation energy is the difference ...
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2 votes
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Can the terms in the microscopic model with nonzero conformal spin generate some new term(s) under RG (renormalization group) flow?

As in the book Bosonization and Strongly Correlated Systems at page 66, it says that "We see that the original perturbation with nonzero conformal spin generates the perturbation with zero conformal ...
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1 answer
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What's the difference between charge density wave and charge ordering for superconductors

So far, my understanding is that they are the same. Charge ordering is a phase transition and the material will have charge density waves once it's in a charge ordered state...? This sounds too simple ...
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22 votes
3 answers
927 views

Why is there a band structure for strongly correlated systems?

The existence of band structure of a crystalline solid comes from the Bloch theorem, which relies on the independent-electron approximation. Why do people still talk about the band structure for a ...
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1 answer
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Coulomb repulsion in the Anderson impurity model

In Phil Anderson's famous paper on impurities, Localized Magnetic States in Metals, he has the following paragraph on page 44, However, I am puzzled by the last sentence: why is the $J$ part really ...
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crystal momentum conservation

Electrons on 1D chain interacting with each other $$ H = \sum_{k_4,k_3, k_2, k_1} V(k_4-k_1) c_{k_4}^{\dagger}c_{k_3}^{\dagger}c_{k_2}c_{k_1}\delta_{k4+k3=k2+k1;\text{mod}~G}$$ where $G$ is ...
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5 votes
1 answer
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Why isn't doped silicon a strongly correlated electron system?

Most books on strongly correlated electrons claim that when the number of itinerant electrons is small and the screening length is large, that the system becomes "strongly correlated", (i.e. the ...
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3 votes
1 answer
200 views

What is the advantage of AdS/CFT in studying strong coupled system comparing with the lattice method

I often heard AdS/CFT correspondence provides a powerful framework to study strong coupled system, which perturbation is not applicable. However, lattice method still works in non-perturbative domain. ...
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