Naslov
Fundamental invariants of many-body Hilbert space

Autori
Sunko, Denis

Izvornik
Modern physics letters B (0217-9849) 30 (2016), 16; 1630009-1

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, pregledni rad, znanstveni

Ključne riječi
Many-body wave functions ; fermion sign problem ; invariant theory.

Sažetak
Many-body Hilbert space is a functional vector space with the natural structure of an algebra, in which vector multiplication is ordinary multiplication of wave functions. This algebra is finite-dimensional, with exactly N!^(d−1) generators for N identical particles, bosons or fermions, in d dimensions. The generators are called shapes. Each shape is a possible many-body vacuum. Shapes are natural generalizations of the ground-state Slater determinant to more than one dimension. Physical states, including the ground state, are superpositions of shapes with symmetric-function coefficients, for both bosons and fermions. These symmetric functions may be interpreted as bosonic excitations of the shapes. The algebraic structure of Hilbert space described here provides qualitative insights into long-standing issues of many-body physics, including the fermion sign problem and the microscopic origin of bands in the spectra of finite systems.

Izvorni jezik
Engleski

Znanstvena područja
Fizika

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