Holographic Geometry of cMERA for Quantum Quenches and Finite Temperature

TL;DR

This paper probes how cMERA encodes holographic geometry for non-ground-state physics, focusing on quantum quenches and finite temperature in free field theories. By computing the cMERA holographic metric $g_{uu}$ and employing a doubled (thermofield) construction, the authors establish qualitative agreement with AdS/CFT expectations such as a half-extended AdS black-hole geometry and the thermofield-double description. They show that quenches drive linear-in-time growth of the interior metric region, while finite temperature yields a matched metric structure, and they reveal infrared enhancements and Fermi-surface features when a chemical potential is present. The results strengthen the view of cMERA as a real-space RG/holographic framework capable of capturing dynamical, thermal, and finite-density phenomena in a controlled, analytic setting.

Abstract

We study the time evolution of cMERA (continuous MERA) under quantum quenches in free field theories. We calculate the corresponding holographic metric using the proposal of arXiv:1208.3469 and confirm that it qualitatively agrees with its gravity dual given by a half of the AdS black hole spacetime, argued by Hartman and Maldacena in arXiv:1303.1080. By doubling the cMERA for the quantum quench, we give an explicit construction of finite temperature cMERA. We also study cMERA in the presence of chemical potential and show that there is an enhancement of metric in the infrared region corresponding to the Fermi energy.

Figures (8)

• Figure 1: The schematic structure of MERA.
• Figure 2: The schematic structure of MERA at finite temperature.
• Figure 3: A plot of $|g(u)|$ as a function of $z=1/k$ for $t=0$ (blue), $t=1$ (red) and $t=2$ (yellow). We chose $\beta=2$ and $\theta_0=0$ at $k=100$.
• Figure 4: A plot of $|g(u)|$ as a function of $z=1/k$ (horizontal coordinate) and $t$ (depth coordinate). We chose $\beta=1$ and $\theta_0=0$ at $k=100$. We plotted the region specified by $0<z<3$ and $0<t<3$.
• Figure 5: Global Structures of AdS Schwarzschild black hole $M_{BH}$ (left) and the gravity dual of quantum quench $M_{Q}$ (right) argued in HaMa. The red horizontal curve denotes time slices we are interested in. Following the Hartle-Hawking prescription, we treat the $t>0$ and $t<0$ region in the Lorentz and Euclidean signature, respectively. The diagonal lines describe the horizons of the black hole. The wavy lines in the top part represents the black hole singularities.