56 research outputs found
Strong planar subsystem symmetry-protected topological phases and their dual fracton orders
We classify subsystem symmetry-protected topological (SSPT) phases in 3 + 1 dimensions (3 + 1D) protected by planar subsystem symmetries: short-range entangled phases which are dual to long-range entangled Abelian fracton topological orders via a generalized “gauging” duality. We distinguish between weak SSPTs, which can be constructed by stacking 2 + 1D SPTs, and strong SSPTs, which cannot. We identify signatures of strong phases, and show by explicit construction that such phases exist. A classification of strong phases is presented for an arbitrary finite Abelian group. Finally, we show that fracton orders realizable via p-string condensation are dual to weak SSPTs, while those dual to strong SSPTs exhibit statistical interactions prohibiting such a realization
Probability distribution of the entanglement across a cut at an infinite-randomness fixed point
We calculate the probability distribution of entanglement entropy S across a
cut of a finite one dimensional spin chain of length L at an infinite
randomness fixed point using Fisher's strong randomness renormalization group
(RG). Using the random transverse-field Ising model as an example, the
distribution is shown to take the form , where , the large deviation function is found explicitly,
and is a nonuniversal microscopic length. We discuss the implications of
such a distribution on numerical techniques that rely on entanglement, such as
matrix product state (MPS) based techniques. Our results are verified with
numerical RG simulations, as well as the actual entanglement entropy
distribution for the random transverse-field Ising model which we calculate for
large L via a mapping to Majorana fermions.Comment: 6 pages, 4 figure
Many-body localization phase transition: A simplified strong-randomness approximate renormalization group
We present a simplified strong-randomness renormalization group (RG) that
captures some aspects of the many-body localization (MBL) phase transition in
generic disordered one-dimensional systems. This RG can be formulated
analytically, and the critical fixed point distribution and critical exponents
(that satisfy the Chayes inequality) are obtained to numerical precision by
solving integro-differential equations. This reproduces many, but not all, of
the qualitative features of the MBL phase transition that are suggested by
previous numerical work and approximate RG studies: our RG might serve as a
"zeroth-order" approximation for future RG studies. One interesting feature
that we highlight is that the rare Griffiths regions are fractal. For thermal
Griffiths regions within the MBL phase, this feature might be qualitatively
correctly captured by our RG. If this is correct beyond our approximations,
then these Griffiths effects are stronger than has been previously assumed.Comment: 10 pages, 5 figures; added references; as in journa
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