About

Xi Dong is an Associate Professor at the Department of Physics at UC Santa Barbara. His research focuses on quantum gravity, string theory, quantum field theory, cosmology, and quantum information theory. As a member of the High Energy Theory group, Professor Dong explores fundamental questions at the intersection of these fields, contributing to the theoretical understanding of the universe at its most fundamental level. His work integrates concepts from quantum information theory with traditional approaches in quantum gravity and cosmology, aiming to uncover deeper insights into the nature of space, time, and matter.

Research topics

• Computer Science
• Mathematics
• Physics
• Mathematical analysis
• Quantum mechanics
• Theoretical physics
• Mathematical physics
• Classical mechanics

Selected publications

• Geometric entropies and their Hamiltonian flows

  Journal of High Energy Physics · 2025-05-09 · 1 citations

  articleOpen access1st authorCorresponding

  A bstract In holographic theories, the Hubeny-Rangamani-Takayanagi (HRT) area operator plays a key role in our understanding of the emergence of semiclassical Einstein-Hilbert gravity. When higher derivative corrections are included, the role of the area is instead played by a more general functional known as the geometric entropy. It is thus of interest to understand the flow generated by the geometric entropy on the classical phase space. In particular, the fact that the associated flow in Einstein-Hilbert or Jackiw-Teitelboim (JT) gravity induces a relative boost between the left and right entanglement wedges is deeply related to the fact that gravitational dressing promotes the von Neumann algebra of local fields in each wedge to type II. This relative boost is known as a boundary-condition-preserving (BCP) kink-transformation. In a general theory of gravity (with arbitrary higher-derivative terms), it is straightforward to show that the flow continues to take the above geometric form when acting on a spacetime where the HRT surface is the bifurcation surface of a Killing horizon. However, the form of the flow on other spacetimes is less clear. In this paper, we use the manifestly-covariant Peierls bracket to explore such flows in two-dimensional theories of JT gravity coupled to matter fields with higher derivative interactions. The results no longer take a purely geometric form and, instead, demonstrate new features that should be expected of such flows in general higher derivative theories. We also show how to obtain the above flows using Poisson brackets.

  PublisherOA PDFDOI

• Entanglement negativity and replica symmetry breaking in general holographic states

  Journal of High Energy Physics · 2025-01-02 · 7 citations

  articleOpen access1st author

  A bstract The entanglement negativity $$ \mathcal{E} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>E</mml:mi> </mml:math> ( A : B ) is a useful measure of quantum entanglement in bipartite mixed states. In random tensor networks (RTNs), which are related to fixed-area states, it was found in ref. [1] that the dominant saddles computing the even Rényi negativity $$ {\mathcal{E}}^{(2k)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>E</mml:mi> <mml:mfenced> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>k</mml:mi> </mml:mrow> </mml:mfenced> </mml:msup> </mml:math> generically break the ℤ 2 k replica symmetry. This calls into question previous calculations of holographic negativity using 2D CFT techniques that assumed ℤ 2 k replica symmetry and proposed that the negativity was related to the entanglement wedge cross section. In this paper, we resolve this issue by showing that in general holographic states, the saddles computing $$ {\mathcal{E}}^{(2k)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>E</mml:mi> <mml:mfenced> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>k</mml:mi> </mml:mrow> </mml:mfenced> </mml:msup> </mml:math> indeed break the ℤ 2 k replica symmetry. Our argument involves an identity relating $$ {\mathcal{E}}^{(2k)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>E</mml:mi> <mml:mfenced> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>k</mml:mi> </mml:mrow> </mml:mfenced> </mml:msup> </mml:math> to the k -th Rényi entropy on subregion AB ∗ in the doubled state $$ {\left.|{\rho}_{AB}\right\rangle}_{A{A}^{\ast }{BB}^{\ast }} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mfenced> <mml:mrow/> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mi>AB</mml:mi> </mml:msub> </mml:mfenced> <mml:mrow> <mml:mi>A</mml:mi> <mml:msup> <mml:mi>A</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:msup> <mml:mi>BB</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:mrow> </mml:msub> </mml:math> , from which we see that the ℤ 2 k replica symmetry is broken down to ℤ k . For k &lt; 1, which includes the case of $$ \mathcal{E} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>E</mml:mi> </mml:math> ( A : B ) at k = 1/2, we use a modified cosmic brane proposal to derive a new holographic prescription for $$ {\mathcal{E}}^{(2k)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>E</mml:mi> <mml:mfenced> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>k</mml:mi> </mml:mrow> </mml:mfenced> </mml:msup> </mml:math> and show that it is given by a new saddle with multiple cosmic branes anchored to subregions A and B in the original state. Using our prescription, we reproduce known results for the PSSY model and show that our saddle dominates over previously proposed CFT calculations near k = 1. Moreover, we argue that the ℤ 2 k symmetric configurations previously proposed are not gravitational saddles, unlike our proposal. Finally, we contrast holographic calculations with those arising from RTNs with non-maximally entangled links, demonstrating that the qualitative form of backreaction in such RTNs is different from that in gravity.

  PublisherOA PDFDOI

• Geometric Entropies and their Hamiltonian Flows

  ArXiv.org · 2025-01-21

  preprintOpen access1st authorCorresponding

  In holographic theories, the Hubeny-Rangamani-Takayanagi (HRT) area operator plays a key role in our understanding of the emergence of semiclassical Einstein-Hilbert gravity. When higher derivative corrections are included, the role of the area is instead played by a more general functional known as the geometric entropy. It is thus of interest to understand the flow generated by the geometric entropy on the classical phase space. In particular, the fact that the associated flow in Einstein-Hilbert or Jackiw-Teitelboim (JT) gravity induces a relative boost between the left and right entanglement wedges is deeply related to the fact that gravitational dressing promotes the von Neumann algebra of local fields in each wedge to type II. This relative boost is known as a boundary-condition-preserving (BCP) kink-transformation. In a general theory of gravity (with arbitrary higher-derivative terms), it is straightforward to show that the flow continues to take the above geometric form when acting on a spacetime where the HRT surface is the bifurcation surface of a Killing horizon. However, the form of the flow on other spacetimes is less clear. In this paper, we use the manifestly-covariant Peierls bracket to explore such flows in two-dimensional theories of JT gravity coupled to matter fields with higher derivative interactions. The results no longer take a purely geometric form and, instead, demonstrate new features that should be expected of such flows in general higher derivative theories. We also show how to obtain the above flows using Poisson brackets.

  PublisherOA PDFDOI

• Holographic tensor networks with bulk gauge symmetries

  Journal of High Energy Physics · 2024-02-28 · 13 citations

  articleOpen access1st authorCorresponding

  A bstract Tensor networks are useful toy models for understanding the structure of entanglement in holographic states and reconstruction of bulk operators within the entanglement wedge. They are, however, constrained to only prepare so-called “fixed-area states” with flat entanglement spectra, limiting their utility in understanding general features of holographic entanglement. Here, we overcome this limitation by constructing a variant of random tensor networks that enjoys bulk gauge symmetries. Our model includes a gauge theory on a general graph, whose gauge-invariant states are fed into a random tensor network. We show that the model satisfies the quantum-corrected Ryu-Takayanagi formula with a nontrivial area operator living in the center of a gauge-invariant algebra. We also demonstrate nontrivial, n -dependent contributions to the Rényi entropy and Rényi mutual information from this area operator, a feature shared by general holographic states.

  PublisherOA PDFDOI

• Entanglement Negativity and Replica Symmetry Breaking in General Holographic States

  arXiv (Cornell University) · 2024-09-19

  preprintOpen access1st authorCorresponding

  The entanglement negativity $\mathcal{E}(A:B)$ is a useful measure of quantum entanglement in bipartite mixed states. In random tensor networks (RTNs), which are related to fixed-area states, it was found in [arXiv:2101.11029] that the dominant saddles computing the even Rényi negativity $\mathcal{E}^{(2k)}$ generically break the $\mathbb{Z}_{2k}$ replica symmetry. This calls into question previous calculations of holographic negativity using 2D CFT techniques that assumed $\mathbb{Z}_{2k}$ replica symmetry and proposed that the negativity was related to the entanglement wedge cross section. In this paper, we resolve this issue by showing that in general holographic states, the saddles computing $\mathcal{E}^{(2k)}$ indeed break the $\mathbb{Z}_{2k}$ replica symmetry. Our argument involves an identity relating $\mathcal{E}^{(2k)}$ to the $k$-th Rényi entropy on subregion $AB^*$ in the doubled state $|{ρ_{AB}}\rangle_{AA^*BB^*}$, from which we see that the $\mathbb{Z}_{2k}$ replica symmetry is broken down to $\mathbb{Z}_{k}$. For $k&lt;1$, which includes the case of $\mathcal{E}(A:B)$ at $k=1/2$, we use a modified cosmic brane proposal to derive a new holographic prescription for $\mathcal{E}^{(2k)}$ and show that it is given by a new saddle with multiple cosmic branes anchored to subregions $A$ and $B$ in the original state. Using our prescription, we reproduce known results for the PSSY model and show that our saddle dominates over previously proposed CFT calculations near $k=1$. Moreover, we argue that the $\mathbb{Z}_{2k}$ symmetric configurations previously proposed are not gravitational saddles, unlike our proposal. Finally, we contrast holographic calculations with those arising from RTNs with non-maximally entangled links, demonstrating that the qualitative form of backreaction in such RTNs is different from that in gravity.

  PublisherOA PDFDOI

• Algebras and Hilbert spaces from gravitational path integrals. Understanding Ryu-Takayanagi/HRT as entropy without AdS/CFT

  Journal of High Energy Physics · 2024-10-08 · 11 citations

  articleOpen access

  A bstract Recent works by Chandrasekaran, Penington, and Witten have shown in various special contexts that the quantum-corrected Ryu-Takayanagi (RT) entropy (or its covariant Hubeny-Rangamani-Takayanagi (HRT) generalization) can be understood as computing an entropy on an algebra of bulk observables. These arguments do not rely on the existence of a local holographic dual field theory. We show that analogous-but-stronger results hold in any UV-completion of asymptotically anti-de Sitter quantum gravity with a Euclidean path integral satisfying a simple and (largely) familiar set of axioms. We consider a quantum context in which a standard Lorentz-signature classical bulk limit would have Cauchy slices with asymptotic boundaries B L ⊔ B R where both B L and B R are compact manifolds without boundary. Our main result is then that (the UV-completion of) the quantum gravity path integral defines type I von Neumann algebras $$ {\mathcal{A}}_L^{B_L} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>A</mml:mi> <mml:mi>L</mml:mi> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>L</mml:mi> </mml:msub> </mml:msubsup> </mml:math> , $$ {\mathcal{A}}_R^{B_R} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>A</mml:mi> <mml:mi>R</mml:mi> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>R</mml:mi> </mml:msub> </mml:msubsup> </mml:math> of observables acting respectively at B L , B R such that $$ {\mathcal{A}}_L^{B_L} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>A</mml:mi> <mml:mi>L</mml:mi> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>L</mml:mi> </mml:msub> </mml:msubsup> </mml:math> , $$ {\mathcal{A}}_R^{B_R} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>A</mml:mi> <mml:mi>R</mml:mi> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>R</mml:mi> </mml:msub> </mml:msubsup> </mml:math> are commutants. The path integral also defines entropies on $$ {\mathcal{A}}_L^{B_L} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>A</mml:mi> <mml:mi>L</mml:mi> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>L</mml:mi> </mml:msub> </mml:msubsup> </mml:math> , $$ {\mathcal{A}}_R^{B_R} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>A</mml:mi> <mml:mi>R</mml:mi> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>R</mml:mi> </mml:msub> </mml:msubsup> </mml:math> . Positivity of the Hilbert space inner product then turns out to require the entropy of any projection operator to be quantized in the form ln N for some N ∈ ℤ + (unless it is infinite). As a result, our entropies can be written in terms of standard density matrices and standard Hilbert space traces. Furthermore, in appropriate semiclassical limits our entropies are computed by the RT-formula with quantum corrections. Our work thus provides a Hilbert space interpretation of the Ryu-Takayanagi entropy. Since our axioms do not severely constrain UV bulk structures, it is plausible that they hold equally well for successful formulations of string field theory, spin-foam models, or any other approach to constructing a UV-complete theory of gravity.

  PublisherOA PDFDOI

• Null states and time evolution in a toy model of black hole dynamics

  arXiv (Cornell University) · 2024-05-07

  preprintOpen access1st authorCorresponding

  Spacetime wormholes can provide non-perturbative contributions to the gravitational path integral that make the actual number of states $e^S$ in a gravitational system much smaller than the number of states $e^{S_{\mathrm{p}}}$ predicted by perturbative semiclassical effective field theory. The effects on the physics of the system are naturally profound in contexts in which the perturbative description actively involves $N = O(e^S)$ of the possible $e^{S_{\mathrm{p}}}$ perturbative states; e.g., in late stages of black hole evaporation. Such contexts are typically associated with the existence of non-trivial quantum extremal surfaces. However, by forcing a simple topological gravity model to evolve in time, we find that such effects can also have large impact for $N\ll e^S$ (in which case no quantum extremal surfaces can arise). In particular, even for small $N$, the insertion of generic operators into the path integral can cause the non-perturbative time evolution to differ dramatically from perturbative expectations. On the other hand, this discrepancy is small for the special case where the inserted operators are non-trivial only in a subspace of dimension $D \ll e^S$. We thus study this latter case in detail. We also discuss potential implications for more realistic gravitational systems.

  PublisherOA PDFDOI

• Constrained HRT Surfaces and their Entropic Interpretation

  Journal of High Energy Physics · 2024-02-21 · 5 citations

  articleOpen access1st authorCorresponding

  A bstract Consider two boundary subregions A and B that lie in a common boundary Cauchy surface, and consider also the associated HRT surface γ B for B . In that context, the constrained HRT surface γ A : B can be defined as the codimension-2 bulk surface anchored to A that is obtained by a maximin construction restricted to Cauchy slices containing γ B . As a result, γ A : B is the union of two pieces, $$ {\gamma}_{A:B}^B $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>γ</mml:mi> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>:</mml:mo> <mml:mi>B</mml:mi> </mml:mrow> <mml:mi>B</mml:mi> </mml:msubsup> </mml:math> and $$ {\gamma}_{A:B}^{\overline{B}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>γ</mml:mi> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>:</mml:mo> <mml:mi>B</mml:mi> </mml:mrow> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:msubsup> </mml:math> lying respectively in the entanglement wedges of B and its complement $$ \overline{B} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> . Unlike the area $$ \mathcal{A}\left({\gamma}_A\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>A</mml:mi> <mml:mfenced> <mml:msub> <mml:mi>γ</mml:mi> <mml:mi>A</mml:mi> </mml:msub> </mml:mfenced> </mml:math> of the HRT surface γ A , at least in the semiclassical limit, the area $$ \mathcal{A}\left({\gamma}_{A:B}\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>A</mml:mi> <mml:mfenced> <mml:msub> <mml:mi>γ</mml:mi> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>:</mml:mo> <mml:mi>B</mml:mi> </mml:mrow> </mml:msub> </mml:mfenced> </mml:math> of γ A : B commutes with the area $$ \mathcal{A}\left({\gamma}_B\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>A</mml:mi> <mml:mfenced> <mml:msub> <mml:mi>γ</mml:mi> <mml:mi>B</mml:mi> </mml:msub> </mml:mfenced> </mml:math> of γ B . To study the entropic interpretation of $$ \mathcal{A}\left({\gamma}_{A:B}\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>A</mml:mi> <mml:mfenced> <mml:msub> <mml:mi>γ</mml:mi> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>:</mml:mo> <mml:mi>B</mml:mi> </mml:mrow> </mml:msub> </mml:mfenced> </mml:math> , we analyze the Rényi entropies of subregion A in a fixed-area state of subregion B . We use the gravitational path integral to show that the n ≈ 1 Rényi entropies are then computed by minimizing $$ \mathcal{A}\left({\gamma}_A\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>A</mml:mi> <mml:mfenced> <mml:msub> <mml:mi>γ</mml:mi> <mml:mi>A</mml:mi> </mml:msub> </mml:mfenced> </mml:math> over spacetimes defined by a boost angle conjugate to $$ \mathcal{A}\left({\gamma}_B\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>A</mml:mi> <mml:mfenced> <mml:msub> <mml:mi>γ</mml:mi> <mml:mi>B</mml:mi> </mml:msub> </mml:mfenced> </mml:math> . In the case where the pieces $$ {\gamma}_{A:B}^B $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>γ</mml:mi> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>:</mml:mo> <mml:mi>B</mml:mi> </mml:mrow> <mml:mi>B</mml:mi> </mml:msubsup> </mml:math> and $$ {\gamma}_{A:B}^{\overline{B}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>γ</mml:mi> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>:</mml:mo> <mml:mi>B</mml:mi> </mml:mrow> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:msubsup> </mml:math> intersect at a constant boost angle, a geometric argument shows that the n ≈ 1 Rényi entropy is then given by $$ \frac{\mathcal{A}\left({\gamma}_{A:B}\right)}{4G} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mrow> <mml:mi>A</mml:mi> <mml:mfenced> <mml:msub> <mml:mi>γ</mml:mi> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>:</mml:mo> <mml:mi>B</mml:mi> </mml:mrow> </mml:msub> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> <mml:mi>G</mml:mi>

  PublisherOA PDFDOI

• Null states and time evolution in a toy model of black hole dynamics

  Journal of High Energy Physics · 2024-08-23 · 3 citations

  articleOpen access1st authorCorresponding

  A bstract Spacetime wormholes can provide non-perturbative contributions to the gravitational path integral that make the actual number of states e S in a gravitational system much smaller than the number of states $$ {e}^{S_{\textrm{p}}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>e</mml:mi> <mml:msub> <mml:mi>S</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:msup> </mml:math> predicted by perturbative semiclassical effective field theory. The effects on the physics of the system are naturally profound in contexts in which the perturbative description actively involves N = O ( e S ) of the possible $$ {e}^{S_{\textrm{p}}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>e</mml:mi> <mml:msub> <mml:mi>S</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:msup> </mml:math> perturbative states; e.g., in late stages of black hole evaporation. Such contexts are typically associated with the existence of non-trivial quantum extremal surfaces. However, by forcing a simple topological gravity model to evolve in time, we find that such effects can also have large impact for N ≪ e S (in which case no quantum extremal surfaces can arise). In particular, even for small N , the insertion of generic operators into the path integral can cause the non-perturbative time evolution to differ dramatically from perturbative expectations. On the other hand, this discrepancy is small for the special case where the inserted operators are non-trivial only in a subspace of dimension D ≪ e S . We thus study this latter case in detail. We also discuss potential implications for more realistic gravitational systems.

  PublisherOA PDFDOI

• A modified cosmic brane proposal for holographic Renyi entropy

  Journal of High Energy Physics · 2024-06-19 · 11 citations

  articleOpen access1st authorCorresponding

  A bstract We propose a new formula for computing holographic Renyi entropies in the presence of multiple extremal surfaces. Our proposal is based on computing the wave function in the basis of fixed-area states and assuming a diagonal approximation for the Renyi entropy. For Renyi index n ≥ 1, our proposal agrees with the existing cosmic brane proposal for holographic Renyi entropy. For n &lt; 1, however, our proposal predicts a new phase with leading order (in Newton’s constant G ) corrections to the cosmic brane proposal, even far from entanglement phase transitions and when bulk quantum corrections are unimportant. Recast in terms of optimization over fixed-area states, the difference between the two proposals can be understood to come from the order of optimization: for n &lt; 1, the cosmic brane proposal is a minimax prescription whereas our proposal is a maximin prescription. We demonstrate the presence of such leading order corrections using illustrative examples. In particular, our proposal reproduces existing results in the literature for the PSSY model and high-energy eigenstates, providing a universal explanation for previously found leading order corrections to the n &lt; 1 Renyi entropies.

  PublisherOA PDFDOI

Recent grants

• Quantum Gravity, Field Theory, and Quantum Information

  NSF · $210k · 2018–2021

Frequent coauthors

• Eva Silverstein

  28 shared

• Gonzalo Torroba

  26 shared

• Bart Horn

  Manhattan College

  23 shared

• Donald Marolf

  University of California, Santa Barbara

  12 shared

• Wayne W. Weng

  University of California, Santa Barbara

  8 shared

• Zhencheng Wang

  8 shared

• Zhaoxin Liang

  Zhejiang Normal University

  7 shared

• Sera Cremonini

  Lehigh University

  7 shared

Labs

• Xi Dong's LabPI

  Not provided

Education

• Ph.D., Physics

  Stanford University

• B.S., Mathematics and Physics

  Tsinghua University