Graduate What are the methods for calculating quantum phase transition?

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The discussion centers on the mathematical methods used to calculate quantum phase transitions. Participants emphasize the importance of having a clearly defined problem to facilitate understanding and calculations. Various mathematical approaches are suggested, but specifics are lacking without context. Clarification on diagrams and their meanings is also requested to enhance comprehension. Overall, a focused question is deemed essential for progressing in the study of quantum phase transitions.
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Trying to understand what the math methods are exist to determine quantum phase transition and how I can calculate it, by what methods.
 
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I don't know what you are talking about and what the meaning of your diagram is. Do you have a concrete physical problem in mind? Asking a clearly defined question is usually more than half way to a solution!
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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