Quantum vs. Classical Phase Transitions

In this section, we give a concise introduction into the theory of quantum phase transitions, emphasizing similarities with and differences from classical thermal transitions. 

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The purpose of this chapter is twofold In the following two sections. Phase Transitions and Critical Behavior and Quantum vs. Classical Phase Transitions, we give a concise introduction into the theory of quantum phase transitions, emphasizing similarities with and differences from classical thermal transitions. After that, we point out the computational challenges posed by quantum phase transitions, and we discuss a number of successful computational approaches together with prototypical examples. However, this chapter is not meant to be comprehensive in scope. We rather want to help scientists who are taking their first steps in this field to get off on the right foot. Moreover, we want to provide experimentalists and traditional theorists with an idea of what simulations can achieve in this area (and what they cannot do,. .. yet). Those readers who want to learn more details about quantum phase transitions and their applications should consult one of the recent review articles or the excellent textbook on quantum phase transitions by Sachdev. ... 

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