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 Jan 11 comment Time reversal symmetry of transverse field Ising model thanks for your ans Teddy Jan 11 accepted Time reversal symmetry of transverse field Ising model Jan 11 comment Time reversal symmetry of transverse field Ising model (continued) find a unitary that brings it real, then the matrix should generically be described by GUE stats (ignoring GSE or other ensembles). All these have nothing to do with whether the Hamiltonian is physically TRS or not, defined by $T = K \prod_i i \sigma_i^y$. Would that be reasonable? Jan 11 comment Time reversal symmetry of transverse field Ising model I am sorry, I do not understand the logic behind defining $T = K$. Where does Reality $\implies$ $T = K$ come from? Maybe the resolution is that the so-called 'TRS' associated with the GOE ensemble is not actually the real, physical TRS; but rather, the fact that the Hamiltonian can be written completely real in an appropriate basis. In other words, if I can find an appropriate unitary transformation that brings a matrix into a completely real form, then it should (generically) be described by GOE stats. That's why rotating the transverse field from x to y is OK. Conversely, if I cannot Jan 11 comment Time reversal symmetry of transverse field Ising model Thank you. Could you elaborate why $T = K$ only and not $T = K \prod_i i \sigma_i^y$? This seems to go against my understanding of what the time reversal operator should do, namely, flip $\vec{S} \to - \vec{S}$. Furthermore, the answer given in this question physics.stackexchange.com/questions/78367/… also agrees with the TR operator I wrote down. Jan 11 revised Time reversal symmetry of transverse field Ising model added 478 characters in body Jan 11 asked Time reversal symmetry of transverse field Ising model Dec 31 awarded Yearling Dec 1 awarded Popular Question Nov 3 awarded Popular Question Aug 24 comment Is the spin 1/2 rotation matrix taken to be counterclockwise? @WetSavannaAnimalakaRodVance no, the mapping is this: let $U$ be an $SU(2)$ matrix (2x2). Then $U S_\mu U^\dagger = \sum_\nu R_{\mu \nu} S_\nu$, where $R$ is an $SO(3)$ matrix (3x3), and $\mu, \nu = x,y,z$. In math speak, the adjoint action of the Lie group $SU(2)$ gives an element of $SO(3)$ in the fundamental rep. In jargony terms, this gives rise to the oft-heard phrase: "SU(2) is the double cover of SO(3)", encapsulated in $SO(3) \cong SU(2)/Z_2$. Jun 26 awarded Nice Answer Jun 18 awarded Notable Question May 24 comment What is many body localization? One should also note that the case of a mobility edge in a Hamiltonian is probably generic: some eigenstates below an energy threshold are MBL while the ones above are thermal, so it is hard to say if MBL is a property of the state or Hamiltonian. May 20 comment Is Chern-number for free fermion system always limited by total band number, i.e. number of orbits with a unit cell? It seems that you can have an arbitrary Chern number (for each of the two bands) even in the Honeycomb lattice: physics.stackexchange.com/questions/45834/… Apr 26 reviewed Approve Why we cannot use Gauss's Law to find the Electric Field of a finite-length charged wire? Apr 18 awarded Popular Question Apr 17 comment Is time reversal symmetry broken in (conventional) superconductors? I'm asking because let's say I'm given a random spin Hamiltonian. Or perhaps random fermionic Hamiltonian. How can I tell if it's time reversal invariant or not? I see many expositions like "because H is invariant under complex conjugation so it is T-invariant"... that doesn't mean anything to me.. How does one define complex conjugation in a basis independent fashion? (For example, the Pauli MATRIX $\sigma^y$ is not-time reversal invariant because of the special basis I've chosen for it, but what's special about this basis? I would like to think of it as obeying the Pauli algebra only) Apr 17 comment Is time reversal symmetry broken in (conventional) superconductors? I don't quite understand why time reversal symmetry is effected as $c_{k \uparrow} \to c_{-k \downarrow}$ and $c_{k \downarrow} \to -c_{-k \uparrow}$... I know this is because of a lack of my conceptual understanding, but how does one define the action of time reversal symmetry on spin variables, fermionic variables, Majorana modes from first principles? Apr 16 revised First and second order phase transitions The previous edit is wrong. Terms like m^3, m^5... are allowed because they explicitly break the symmetry. That is how you model a FIRST order phase transition. sigh.. To maintain positive-definiteness the largest power must be even.