Exact holographic mapping and emergent space-time geometry

By Xiao-Liang Qi. 2013

178 citations recorded by the source corpus.

In this paper, we propose an {\it exact holographic mapping} which is a unitary mapping from the Hilbert space of a lattice system in flat space (boundary) to that of another lattice system in one higher dimension (bulk). By defining the distance in the bulk system from two-point correlation functions, we obtain an emergent bulk space-time geometry that is determined by the boundary state and the mapping. As a specific example, we study the exact holographic mapping for $(1+1)$-dimensional lattice Dirac fermions and explore the emergent bulk geometry corresponding to different boundary states including massless and massive states at zero temperature, and the massless system at finite temperature. We also study two entangled one-dimensional chains and show that the corresponding bulk geometry consists of two asymptotic regions connected by a worm-hole. The quantum quench of the coupled chains is mapped to dynamics of the worm-hole. In the end we discuss the general procedure of applying this approach to interacting systems, and other open questions.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f06b508e36f22089e82df1a7e95d0ec12b821802

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. R. Myers
2. T. Takayanagi
3. J. Sully
4. L. Susskind
5. D. Harlow
6. R. Cai
7. Masamichi Miyaji
8. D. Stanford

In Nuclear and High Energy Physics

1. R. Myers
2. D. Harlow
3. D. Stanford
4. T. Takayanagi
5. J. Sully
6. L. Susskind
7. Guy F. de Téramond
8. Masamichi Miyaji

In Statistical and Nonlinear Physics

1. R. Myers
2. T. Takayanagi
3. J. Sully
4. D. Harlow
5. Masamichi Miyaji
6. B. Czech
7. L. Susskind
8. D. Stanford

Citations in the corpus

• Light-front holographic QCD and emerging confinement (2014, background): “Other approaches to emergent holography are discussed in [101, 102, 103, 104, 105].”
• Neural Network Renormalization Group (2018, methodology): “[68] Xiao-Liang Qi, “Exact holographic mapping and emergent”
• Introduction to holographic superconductor models (2015, background): “A very new perspective was proposed, which is called the exact holographic mapping [6].”
• Integral geometry and holography (2015, background): “3 The The analogy between holography and tensor networks was further advanced in [22–26]; see also [27] for a critique of associating MERA directly with the spatial slice of AdS3.”
• Computational complexity and black hole horizons (2014, background): “The stretching phenomenon was discussed in [31, 32] and is illustrated in Fig.”
• Space from Hilbert Space: Recovering Geometry from Bulk Entanglement (2016, background): “At the same time, if we have some dual bulk fields living in AdS whose ground state is presumably also short range entangled [10], then it may in turn be described by a RC”
• Surface/State Correspondence as a Generalized Holography (2015, background): “Its has been conjectured in [4] (see also [5] for a modified version of this conjecture) that the AdS/CFT can be interpreted as a real space renormalization flow called entanglement renormalization or MERA [6].”