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Undergrad turned grad


1d
revised Addition of spins and projection
edited title
1d
revised Addition of spins and projection
deleted 13 characters in body
1d
comment Addition of spins and projection
@EmilioPisanty as an example, consider $S_1$ and $S_2$ to be spin-1/2s. The combined Hilbert space splits into a spin-1 and spin-0 sector. The projection onto the spin-1 sector is given by $P_{12}^1 = (3 + 4 \vec{S}_1\cdot \vec{S}_2)/4$. The same can be done for arbitrary spins $S_1, S_2$.
1d
comment Addition of spins and projection
well let's say it's my claim. Didn't I say exactly how $P^S_{12}$ is defined? It's the projection onto the spin-$S$ subspace of the tensor product of the Hilbert spaces of $S_1$ and $S_2$.
1d
asked Addition of spins and projection
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.
Mar
24
comment Double semion model on a square lattice
Hi @No.9999, I'm interested in the correct form of the double semion Hamiltonian on the square lattice. May I know what it is? Thanks.
Jan
7
awarded  Popular Question
Dec
31
awarded  Yearling
Nov
28
revised The spin and weight of a primary field in CFT
edited body
Oct
18
comment Time evolution operator of a periodic Hamiltonian
Which static Hamiltonian do you mean? You can find $H_{eff}$ by solving the Dyson series for the evolution operator (or a Magnus expansion), and you can truncate the series at some order to get an approximation. But let's say that you manage to find $H_{eff}$ exactly. Then if you view the system in stroboscopic time (periods of $T$), the system looks exactly like it involves under the static Hamiltonian $H_{eff}$, that's not an approximation.