Abstract
The quantum solid-on-solid (SOS) model for the free surface of a crystal is studied at zero and finite temperatures. In addition to the usual roughening transition, this model also exhibits a superfluid transition. The phase diagram is constructed. We also formulate and study a quantum SOS model for the solid-liquid interface, which takes into account the motion and the compressibility of the liquid and solid. The existence of a phase transition at zero temperature is shown. The phases differ in the form of the excitation spectrum. In both interface models the interface at zero temperature is smooth. The quantum effects only slightly reduce the temperature of the roughening transition in comparison to the classical value.
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