Exactly Solvable Models in Arbitrary Dimensions

TL;DR

This paper introduces a new class of quasi-exactly solvable many-body Hamiltonians in arbitrary dimensions, allowing for customizable ground state correlations, including known and novel types.

Contribution

It constructs a general framework for many-body Hamiltonians with customizable ground state correlations across arbitrary dimensions, including new models with unique correlations.

Findings

Reproduces known correlations in 1D and 2D

Introduces new models with novel correlations in higher dimensions

Provides explicit examples of solvable many-body Hamiltonians

Abstract

We construct a new class of quasi-exactly solvable many-body Hamiltonians in arbitrary dimensions, whose ground states can have any correlations we choose. Some of the known correlations in one dimension and some recent novel correlations in two and higher dimensions are reproduced as special cases. As specific interesting examples, we also write down some new models in two and higher dimensions with novel correlations.