# 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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### Confusion on Hamiltonian unbounded from below and Ostrogradsky Instability

This might be a silly question but I failed to get it. In Ostrogradsky Instability, we deduced that Lagrangian of higher-order derivatives leads to Hamiltonian linear to canonical momenta, and thus, ...
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### Questions of lower boundness of Hamiltonians in quantum theories

In general spectral analysis, we have examples of unbounded from below hamiltonians with discrete spectrum. Is it okay to say that they have no sense in physical context, because for me it looks like ...
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### Ground state energy of infinite Heisenberg XXX model with open or periodic boundary conditions equal?

I was wondering if there is anywhere a formal proof that shows that the ground state energy of a Heisenberg XXX model with periodic boundary conditions becomes equal to the ground state energy with ...
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### Diagonalize a many-body Hamiltonian

Assume we start with a generic many-body Hamiltonian: $$H=\sum_{ij} t_{ij} a_i^\dagger a_j+\sum_{mnlk}U_{mnkl}a_{m}^{\dagger}a_{n}^{\dagger}a_la_k.$$ Now if there is only the one-body part, which ...
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### Expectation value of non-interacting groundstate

Assume that I have a tight binding model given in second quantized form as follows; \begin{equation} H = \sum_i f_i^{\dagger}f_i + t \sum_{i,j} f_i^{\dagger}f_j \end{equation} In real space, ...
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### On the existence of ground state for a free particle

Given a free particle, the ground state of the system is the eigenstate with zero momentum. However, we also know that momentum operator does not have proper eigenstates, but rather it's spectrum is ...
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