Questions tagged [ground-state]

The ground state of a quantum/classical mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. When a quantum system has infinite possible ground states, it is gapless with massless modes; if a quantum system has finite ground states, it is known as gapped and potentially topologically ordered. The ground state of a quantum field theory is usually called the vacuum state or the vacuum.

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What's the momentum-space vacuum wave-functional of a fermion?

In the Schrödinger picture, the field eigenstates of a real scalar field $\hat\phi(\mathbf x)$ with $\mathbf x \in\mathbb R^3$ are the states $\hat\phi(\mathbf x)|\Phi\rangle=\Phi(\mathbf x)|\Phi\...
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Finding mathematically the ground state density in DFT

I've posted this question in the chemistry exchange, but it did not get any answer; maybe it is better suited here? To find the ground state density in DFT, you set the following Lagrangian: $$L = E[...
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Showing in the classical limit an operator $U = \langle \Omega | U |\Omega \rangle$

Let $\Omega$ be the ground state of the Hilbert space $\mathcal H$. How can I show that in the classical limit, an operator $U$ goes to $ \langle \Omega | U |\Omega \rangle$? Attempt. This is ...
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Cosmic strings and ground state degeneracy in SSB

There are two conflicting perceptions that I have regarding the notion of ground state post-SSB. Consider the Higgs mechanism e.g. for the electroweak theory. On the one hand, we say that the vacuum ...
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The “Hartree-Fock energy” in the Feynman formalism vs the Hartree-Fock method

This question has been previously asked, but I do not understand the answer. When calculating the ground state energy of an interacting system by a perturbative expansion in terms of Feynman diagrams,...
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How to actually find a Hartree-Fock ground state?

I am interested in finding the Hartree-Fock ground state for a system of interacting fermions (with totally local scattering, so a delta-function interaction potential). I have read through some ...
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What's the ground state wave-functional of a fermion?

The vacuum state, free field wave-functional of a scalar field $\hat\phi(x)$ in the Schrödinger representation of quantum field theory is $$\begin{array}{cl} \Psi_0[\phi] &= C\prod_k e^{-\omega(k)...
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In the ground state properties of electron gas, is $V$ the volume of all the metal or the volume of a cell of the lattice?

In the ground state properties of electron gas (Sommerfeld theory), is $V$ the volume of all the metal or the volume of a cell of the lattice? I thought the latter because the Born—von Karman boundary ...
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Why are degenerate ground states interesting?

Studying the Su-Schrieffer-Heeger chain I have learned that the model has two different phases, one which is called topological and the other one trivial. In the notes it says that these phases are ...
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Hamiltonian and Supercharges

Mirror Symmetry p.188 Eq. 10.109 states that $$H \left\vert \alpha\right> = 0 \Longleftrightarrow Q \left\vert\alpha\right> = \overline{Q} \left\vert\alpha\right> =0. \tag{10.109}$$ I dont ...
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Energy level below ground state

Can an electron occupy an energy level lower than its ground state? Do electrons come closer to each other at 0K temperature?
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SUSY Breaking in the Vacuum

Under what conditions is supersymmetry preserved in the vacuum state? In particular, suppose I have some super potential $W(x)$ which does not permit normalizable ground-state wave functions (such as $...
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Cycle of radiation

The second is defined as the duration of 9,192,631,770 cycles of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom. So what is ...
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Supersymmetry Perturbation Theory

Source:Mirror Symmetry p.198 I have the Hamiltonian $$H = \lambda\bigg( \frac{1}{2} \tilde{p} + \frac{1}{2}h''(x_i)^2(\tilde{x}-\tilde{x_i})^2 + \frac{1}{2}h''(x_i)[\overline{\psi}, \psi] \bigg) + \...
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How to ascertain that the Rayleigh-Ritz variational method gives the exact value of the ground state energy?

So the Rayleigh-Ritz variational method can be used to calculate the ground state energy of a quantum system. If $\phi(x)$ is a suitable (square integrable) and normalised function of the coordinates ...
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How to derive the Galitski-Migdal formula from the definition of zero temperature Green's function?

Usually, in condensed matter physics the zero temperature Green's function is defined as: $$G(x,t,x',t')=-i \langle 0| \psi(x,t) \psi^\dagger (x',t')|0\rangle \qquad x\equiv(\vec{r},s)$$ in which $| 0 ...
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Choosing approximate eigenfunctions

In the variational approach of estimating the ground state energy of a system we choose an approximate eigenfunction dependent on certain parameters and then minimize the expectation value of the ...
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Schrodinger's Equation in three dimensions

Consider Schrödinger's Equation, $$H=\sum^3_{i=1} \frac{p^2_i}{2m_i}+V(x_1,x_2,x_3).$$ In one dimensional case, we can analyse the shape of the potential, i.e $$V(x)=\frac{1}{2}m_1 \omega^2_1 x^2$$ ...
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Spin-1 Heisenberg model, the AKLT model, and their ground states

I am reading literature on quantum spin chains and matrix product states, and I notice similar arguments regarding the spin-1 antiferromagnetic Heisenberg model, $H_{H} = \sum_i S_i \cdot S_{i+1}$, ...
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Accuracy of Heisenberg Uncertainty Principle for estimating ground state energy of particle in potential well

I've understood the assumptions and logic behind the 'proof' that the ground state of a particle in an infinite potential well has a non-zero energy using the Heisenberg Uncertainty Principle. ...
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$k$-local Hamiltonian with long range entangled ground states?

Is it possible, and if yes, is there a relatively simple example of a Hamiltonian that only has k-local terms but its ground state always has entanglement beyond $k$ sites? For instance if $H = H_{...
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What is ground state useful for?

Many textbooks and research are oriented to computing or finding the ground state of a quantum mechanical system. Why is it such a big deal? What can be done once one has the ground state?
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What is the “lowest energy”?

In many textbooks I come across the term lowest energy. For example in atomic structures, electrons are placed in orbitals in order for the atom to have the lowest energy. But what is this energy? ...
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Is the ground state a Schrödinger cat state?

Consider the following Bose-Hubbard Hamiltonian which describes a Bose-Einstein condensate confined in a two-well potential: $$ H= -T(a_L^\dagger a_R + a_L a_R^\dagger ) + \frac{U}{2}(n_L^2+n_R^2-...
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Physical meaning that an energy functional has no minimizer

It is well known that the Hamiltonian of a system might not have a minimizer, even the Hamiltonian is bounded below. For example, let us consider the cubic time independent Schrödinger equation \begin{...
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Question about fundamental states on an finite well

My question is the following, when we search for the bound states a finite well potential we have solutions symmetric and antisymmetric so we get two families of solutions. In this case, the ...
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Why does a system assume ground state at absolute zero temperature?

I am going through Huang, Statistical Mechanics. He says at 0 kelvin, a quantum system assumes ground state so that $S=k_B ln(G)$ holds where $G$ is the degeneracy of the ground state . My question ...
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What happens to a particle in a well if the well is made bigger? [duplicate]

Let's say we have a particle in an infinite well, and let's also say it is in the ground state. Now we make the well bigger by very quickly moving one of the boundaries of the well. How do we ...
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Topological materials and fractionalized excitations

I've been told several times that topological materials (such topological insulators) must have "fractionalized" excitations. Equivalently, if a material does not have fractionalized excitations, it ...
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How does the normalization of an $n$-particle state $|n_{\mathbf{k}}\rangle$ work?

You can expand the free, real scalar field in the following manner $$ \phi(x) = \int \frac{d^{3}\mathbf{k}}{(2\pi)^3} \frac{1}{\sqrt{2\omega_{\mathbf{k}}}} \bigg[ e^{- i \omega_{\mathbf{k}}x^0+i \...
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Triplet states and the Hund's rule in identifying the ground state configuration (open shell)

I referred to some of the questions about Hund's rule on StackExchange, such as this for example, but still wasn't able to have my question resolved. (the wikiepdia page has $E_{ex} = C - \frac{1}{2}...
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Supposing that a quantum system is in a degenerate ground-state, is it valid to call this a “superposition” of the possible groundstates?

According to the adiabatic theorem, a quantum system can be prepared in the ground-state of some Hamiltonian $H_f$ if it starts in the ground state of some Hamiltonian $H_I$ and is varied "slowly" ...
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Simple iterative method to obtain any ground state given Hamiltonian operator

So, I'm considering the operator $\frac{h_0}{\bf H}$ with $\bf H$ any hamiltonian operator and $h_0$ a small non-zero positive constant with dimensions of energy and assumed to bound by below all ...
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How can I differentiate ground state and excited state hadrons?

How can I differentiate ground state and excited state hadrons ? What is the difference between their quantum numbers?
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Lagrangian multiplier and ground state search

I'm trying to understand the paper of Schollwoeck. On page 64, equation 203 he states: In order to solve this problem, we introduce a Lagrangian multiplier λ, and extremize $$ \langle \psi | ...
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Whether to add the chemical potential in the 2nd quantized Hamiltonian (Piers Coleman)

I am reading the Piers Coleman's book : Introduction to Many-body Physics. And I am now struggling with the construction of the 2nd quantized Hamiltonian. Typically I don't know whether to add the ...
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2 Particles in a Landau level interacting via a Central Potential

I am studying Robert Laughlin's paper about the Franctional Quantum Hall Effect http://gtwlx.jpkc.fudan.edu.cn/reference/FQHE-T.pdf . In it, while he is setting up his motivation for the Laughlin ...
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Ground state degeneracy [closed]

Today, I have learned from Prof. Cramer's (univ. of minnesota) lecture that the ground state can have degeneracy. and he showed entropy $S = k_{b} ~ ln_{}~ \bf{n}$ , if ground state is $\bf{n} $ - ...
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Problem with interaction ground state in Peskin and Schroeder (Chapter 4)

In Peskin and Schroeder Section 4.2, in the process of deriving the form of the interacting ground state, the authors seem to add an extra factor $e^{iH_0(T+t_0)}$ in the second line of eq 4.28 (...
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Is ground state and vacuum state the same thing?

Vacuum state is the lowest possible quantum energy state but isn't this also the definition of the ground state?
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Energy of an electron in triangle potential [duplicate]

I'm trying to get the fundamental state of an electron in a potential, as in: $$V(X)=e|x|$$ Where $e$ is a constant. To start with I want to solve it with $e=1$, then where $e$ is big enough that it ...
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ground state of spin chain with $Z_i X_{i+1} Z_{i+2}$ interaction

the problem comes from transverse field Ising model, with an extra 3-spin interaction term $$H=H_0+H_1+H_2=-h\sum_{i=1}^{N}X_i -\lambda_1 \sum_{i=1}^{N-1}Z_i Z_{i+1}-\lambda_2 \sum_{i=1}^{N-2}Z_i X_{i+...
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Why is the ground state energy of particle in a box not zero?

I understand that we want to solve for non-zero values of wave function. I always thought that is to avoid the obvious answer to Schrodinger equation. But from physical standpoint, if we have a ...
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For the ground state of tin, why is it not possible to have a triplet D state?

I have been looking at electron configuration and understand the use of hund's rules, the Aufbau principle and the Pauli exclusion principle but am having difficulty with a question that has come up ...
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Grounds state of carbon - Hunds Rule

I have a question about Hund's second rule for the ground state of carbon. Why is it that when S=1, L has to be 1 instead of 2? I don't get the whole symmetric/ antisymmetric argument. Why is L=2 ...
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Renormalization group to predict the ground state of a Hamiltonian

It is slightly difficult to phrase my question because I'm looking more of an entry point to something I know is a large field rather than a solution to a specific problem. I occasionally see papers ...
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What phase of an electromagnetic wave is the ground state?

I have read that the uncertainty principle applies to electromagnetic radiation, and the ground state could not be sitting on the lowest energy point, because then it would have definite position and ...
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Position probability distribution of a particle in an infinite square well: classical versus quantum

The wave-function for a single particle in a potential well of width $L$ is given by the relation $$\Psi_n(x)=\sqrt{\frac 2L} \sin(K_n x)$$ where $K_n$ is $(n+1)\pi/L$ and $n$ is a positive integer. ...
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Ground state of electrons in diatomic molecule and probability to find electron near a shell at the ground state

Question: The effective Hamiltonian of an outer-shell electron in a diatomic molecule is given by $$H = \left(\begin{array}{cc} E_1 & t \\ t & E_2 \\ \end{array} \right)$$ where $E_1$ ...
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How to get ground state wave function in path integral method?

For a fermion field with the nearest interaction on a square lattice. How once could determine ground state field or ground state wave function in path integrals? In general how one can determine wave ...