A theory paper predicts the zero- and finite-temperature phase diagram of one-dimensional bosons with power-law hopping, including a divergent Tomonaga-Luttinger exponent for 2<α<3 at low temperature.
The absence of finite-temperature phase transitions in low-dimensional many-body models: a survey and new results
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abstract
After a brief discussion of the Bogoliubov inequality and possible generalizations thereof, we present a complete review of results concerning the Mermin-Wagner theorem for various many-body systems, geometries and order parameters. We extend the method to cover magnetic phase transitions in the periodic Anderson Model as well as certain superconducting pairing mechanisms for Hubbard films. The relevance of the Mermin-Wagner theorem to approximations in many-body physics is discussed on a conceptual level.
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One dimensional Bose-Hubbard model with long range hopping
A theory paper predicts the zero- and finite-temperature phase diagram of one-dimensional bosons with power-law hopping, including a divergent Tomonaga-Luttinger exponent for 2<α<3 at low temperature.