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Apr
24
comment Addition of $N$ spin halves
it is ! thanks! :)
Apr
24
asked Addition of $N$ spin halves
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)