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We introduce a general analytic approach to the study of factorization points and factorized ground states in quantum cooperative systems. The method allows to determine rigorously existence, location, and exact form of separable ground states in a large variety of, generally non-exactly solvable, spin models belonging to different universality classes. The theory applies to translationally invariant systems, irrespective of spatial dimensionality, and for spin-spin interactions of arbitrary range.
Frustration in quantum many body systems is quantified by the degree of incompatibility between the local and global orders associated, respectively, to the ground states of the local interaction terms and the global ground state of the total many-bo
We study the Killing vectors of the quantum ground-state manifold of a parameter-dependent Hamiltonian. We find that the manifold may have symmetries that are not visible at the level of the Hamiltonian and that different quantum phases of matter exh
The ground state of solid $^4$He is studied using the diffusion Monte Carlo method and a new trial wave function able to describe the supersolid. The new wave function is symmetric under the exchange of particles and reproduces the experimental equat
We study a quantum quench of the mass and the interaction in the Sinh-Gordon model starting from a large initial mass and zero initial coupling. Our focus is on the determination of the expansion of the initial state in terms of post-quench excitatio
Statistical mechanics of 1D multivalent Coulomb gas may be mapped onto non-Hermitian quantum mechanics. We use this example to develop instanton calculus on Riemann surfaces. Borrowing from the formalism developed in the context of Seiberg-Witten dua