arXiv subjects

Xuchen Cao

Publications and source records attributed to Xuchen Cao.

4 recordsLinked to original sources

arXiv2025

Gravitational Algebras with Two Areas

We study gravitational algebras on spacetimes with two extremal surfaces. In the example of a long wormhole with two asymptotic AdS boundaries and two compact extremal surfaces, we discuss the assignment of gravitational algebras to various regions bounded by the extremal surfaces and/or asymptotic boundaries. Using the split property, we construct type II algebras from the crossed product in the left exterior, right exterior, the middle ``python's lunch'' region, and their complement regions. We also study the case where only the area sum operator or area difference operator is included as part of the gravitational algebra. This can be achieved by picking the appropriate microcanonical ensemble, and these gravitational algebras can either be type II or type III depending on the region. In the case where we include only the area difference mode, the crossed product gives rise to a weight that restricts to a trace on the middle region. Differences of relative entropies with respect to this weight give differences in generalized entropies. This provides an algebraic understanding of the order parameter that controls the phase transitions between entanglement wedges. We emphasize the role of operator-valued weights used in our construction.

hep-th↗

arXiv2025

Single-Sided Black Holes in Double-Scaled SYK Model and No Man's Island

We study a single-sided black hole with an end-of-the-world (EoW) brane behind the horizon in the double-scaled SYK (DSSYK). The new Hamiltonian is a deformation of the original DSSYK Hamiltonian with an extra exponential wormhole length operator, which leads to a new chord diagram rule. The boundary algebra is defined as generated by the new Hamiltonian and boundary matter. There is an alternative but equivalent definition with a $q$-coherent state due to a nontrivial isomorphism of the vN algebra of DSSYK. This isomorphism induces a unitary equivalence, which yields a surprising result that the boundary algebra of a single-sided black hole in DSSYK has a non-trivial commutant and is a type II$_1$ vN factor. It follows that the full bulk reconstruction from the boundary is impossible, and there is a ``no man's island" behind the horizon in the semiclassical JT limit. Inspired by the EoW brane, we construct a family of matter-brane states with an arbitrary number of matter chords and behaving like an EoW brane. They exactly solve the full spectrum of DSSYK. We take different ways to understand the nontrivial commutant. We show that the commutant is complex on chord number basis and thus non-geometric. In the semiclassical JT limit, the commutant becomes the canonical purification of the boundary algebra and claims the no man's island. In the context of Hawking radiation after Page time, the unitary equivalence is interpreted as encoding the canonical purification into the old Hawking radiation, and the no man's island has the same essence as the island. Including the exponential wormhole length operator independently, the boundary algebra is extended to all bounded operators and reconstructs the no man's island. This can be regarded as a different choice for the definition of boundary algebra. This type I$_\infty$ algebra is closely related to the EoW brane in Kourkoulou-Maldacena.

hep-th↗

arXiv2024

Ramp from Replica Trick

We compute the spectral form factor of the modular Hamiltonian $K=-\lnρ_A$ associated to the reduced density matrix of a Haar random state. A ramp is demonstrated and we find an analytic expression for its slope. Our method involves an application of the replica trick, where we first calculate the correlator $<\text{tr}ρ_A^n\;\text{tr}ρ_A^m>$ at large bond dimension and then analytically continue the indices $n,m$ from integers to arbitrary complex numbers. We use steepest descent methods at large modular times to extract the ramp. The large bond dimension limit of the replicated partition function is dominated by a sum over \emph{annular non-crossing permutations}. We explored the similarity between our results and calculations of the spectral form factor in low dimensional gravitational theories where the ramp is determined by the double trumpet geometry. We find there is an underlying resemblance in the two calculations, when we interpret the annular non-crossing permutations as representing a discretized version of the double trumpet. Similar results are found for an equilibrated pure state in place of the Haar random state.

hep-th↗

arXiv2022

Topological Field Theories of Three-Dimensional Rotation Symmetric Insulators: Coupling Curvature and Electromagnetism

Quantized responses are important tools for understanding and characterizing the universal features of topological phases of matter. In this work, we consider a class of topological crystalline insulators in $3$D with $C_n$ lattice rotation symmetry along a fixed axis, in addition to either mirror symmetry or particle-hole symmetry. These insulators can realize quantized mixed geometry-charge responses. When the surface of these insulators is gapped, disclinations on the surface carry a fractional charge that is half the minimal amount that can occur in purely $2$D systems. Similarly, disclination lines in the bulk carry a fractionally quantized electric polarization. These effects, and other related phenomena, are captured by a $3$D topological response term that couples the lattice curvature to the electromagnetic field strength. Additionally, mirror symmetric insulators with this response can be smoothly deformed into a higher-order octopole insulator with quantized corner charges. We also construct a symmetry indicator form for the topological invariant that describes the quantized response of the mirror symmetric topological crystalline insulators, and discuss an unusual response quantization in time-reversal breaking systems.

cond-mat.str-el↗