Exactly solvable models for two-dimensional quantum systems

We study a family of exactly solvable models of conformally invariant quantum field theory in D-dimensional space. We demonstrate the existence of D-dimensional analogs of primary and secondary fields. Under the action of the energy–momentum tensor and conserved currents, the primary field creates an infinite set of (tensor) secondary fields of different generations. The commutators of secondary fields with zero components of the current and energy–momentum tensor include anomalous operator terms. We show that the Hilbert space of conformal theory has a special sector whose structure is solely defined by the Ward identities independently of the choice of dynamical model. The states of this sector are constructed from secondary fields. Definite self-consistent conditions on the states of the latter sector fix the choice of the field model uniquely. The above self-consistent conditions are formulated as follows. Special superpositions Qs, s= 1, 2, …, of secondary fields are constructed. Each superposition is determined by the requirement that the form of its commutators with energy–momentum tensor of a primary fiel d. Each equation Qs(x)=0 is consistent, and defines an exactly solvable model for D ≥ 3. The structure of these models is analogous to that of well-known two-dimensional conformal models. The states Qs(x)|0> are analogous to the null vectors of two-dimensional theory. In each of these models one can obtain a closed set of differential equations for all the higher Green functions, as well as algebraic equations relating the scale dimension of the fundamental field to the D-dimensional analog of a central charge. As an example, we present a detailed discussion on a pair of exactly solvable models in even-dimensional space D≥4.

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Generalized Generalized Spin Models Associated with Exactly Solvable Models

Progress in Algebraic Combinatorics ◽

10.2969/aspm/02410081 ◽

2018 ◽

Author(s):

Tetsuo Deguchi

Keyword(s):

Exactly Solvable Models ◽

Solvable Models ◽

Spin Models ◽

Exactly Solvable

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Interaction between Different Kinds of Quantum Phase Transitions

Quantum Reports ◽

10.3390/quantum3020015 ◽

2021 ◽

Vol 3 (2) ◽

pp. 253-261

Author(s):

Angel Ricardo Plastino ◽

Gustavo Luis Ferri ◽

Angelo Plastino

Keyword(s):

Phase Transitions ◽

Nuclear Physics ◽

Body Problem ◽

Quantum Phase Transitions ◽

Quantum Phase ◽

Exactly Solvable Models ◽

Solvable Models ◽

Many Body ◽

Pairing Interaction ◽

Exactly Solvable

We employ two different Lipkin-like, exactly solvable models so as to display features of the competition between different fermion–fermion quantum interactions (at finite temperatures). One of our two interactions mimics the pairing interaction responsible for superconductivity. The other interaction is a monopole one that resembles the so-called quadrupole one, much used in nuclear physics as a residual interaction. The pairing versus monopole effects here observed afford for some interesting insights into the intricacies of the quantum many body problem, in particular with regards to so-called quantum phase transitions (strictly, level crossings).

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