# Gravity, Quantum Fields and Information

**The aim of the independent research group “Gravity, Quantum Fields and Information” (GQFI), led by Dr. Michal P. Heller, is to explore the fascinating interplay between general relativity, quantum field theory, and quantum information theory uncovered in recent years, using insights from holography (AdS/CFT), many-body physics, black holes, and more.**

Some of the motivating questions for GQFI are:

- Can we understand the dynamical geometry of spacetime, and hence gravity itself, as an emergent quantum-many body phenomenon, in the spirit of “It from Qubit”? And what role do quantum information concepts such as entanglement and complexity play in this connection?

- Quantum systems with many constituents are known to be very complex, and require powerful computers to simulate. Can we use new ideas from tensor networks to finding efficient ways to model these systems on a computer?

- Black holes are the only known objects in nature in which both quantum theory and general relativity are simultaneously relevant, and therefore serve as a true “theorists laboratory” for quantum gravity. Can we use tools from holography and algebraic quantum field theory to shed light on these mysterious objects, and perhaps reveal their interior?

- How do novel methods and connections aid us in modeling equilibration processes like those occurring in ultra-energetic collisions of atomic nuclei at RHIC and LHC accelerators?

Here are some of the specific research projects currently being pursued by GQFI:

**Complexity in quantum field theory**

In the context of holography, the quantum information-theoretic notion of complexity has been conjectured to encode certain gravitational quantities capable of probing the interior of AdS black holes. Members of our group have pioneered the effort to make this idea precise in quantum field theories, and we continue with the study of this novel quantity in a variety of models and settings. Our group's first works in this direction delved into the study of complexity in the context non-equilibrium quantum dynamics [1] and thermofield double states in free scalar quantum field theories [2]. Subsequent efforts have ranged from interpreting the parallel notion of path-integral complexity as a quantum circuit in (1+1) conformal field theories [3], to studying state and operator complexity in the same set-up [4,5], to characterizing universal properties of complexity for mixed states corresponding to vacuum subregions of free theories [6] and proposing that finite spacetime regions correspond to quantum circuits with a complexity given by the on-shell value of the gravitational action [7]. With our studies we hope to pave the way for a better understanding of complexity in quantum field theories and to identify its precise role in the emergence of spacetime in holography.

**Tensor networks**

Tensor networks are extremely useful tools for representing certain quantum states, and have interesting geometric properties that have led to fruitful analogies with holography. In particular, the MERA tensor network, which is naturally suited to represent 1D critical systems (described by CFTs), has a 2D negatively curved geometry, and has been conjectured to describe certain aspects of the AdS/CFT correspondence. Can insights from gravity and holography be useful to strengthen this connection, or to design new, more powerful tensor networks for simulating complex quantum systems, e.g., by taking advantage of symmetrical aspects?

**Entanglement structure & modular flow**

We are investigating the properties of modular (entanglement) Hamiltonians for low dimensional systems [8,9]. In particular, we have focused on understanding the transition from locality to continuous non-locality in the modular flow [10]. This may provide new insights into the problem of bulk reconstruction in holography.

**Black hole interiors **

Quantum Extremal Islands are special regions of spacetime that play an important role in relation to the entropy of black holes. Thus, they are closely connected to the black hole information paradox, which is of fundamental importance in our attempts to combine quantum mechanics and gravity. We are investigating the properties of quantum extremal islands in various models [11,12], with a current focus on questions relating to the black hole interior.

**Non-equilibrium dynamics**

**Other activities**

The GQFI group is engaged in a number of other activities aimed to further collaboration, communication, and general interest in physics. We run a series of weekly virtual seminars together with the String Theory group at the University of Warsaw as well as our QGI seminar series on quantum gravity and information with University of Amsterdam and UCL, and the HEP-TN seminar series dedicated to tensor networks in high-energy physics. Interested researchers from other groups can tune-in and participate interactively. The talks are subsequently posted to our YouTube channel so that anyone can view them freely, anytime. We also host a topical “GQFI Workshop” twice a year; links to past events can be found on the right side of the page. Additionally, members of our group are engaged in various outreach activities, such as local Science Day events. To keep up with the latest news and developments, check out our Twitter feed!

**References**

Most of our group's publications can be found on INSPIRE-HEP.

- Hugo A. Camargo, Pawel Caputa, Diptarka Das, Michal P. Heller, Ro Jefferson: "Complexity as a novel probe of quantum quenches: universal scalings and purifications", Phys. Rev. Lett. 122, 081601 (2019), DOI: 10.1103/PhysRevLett.122.081601, arXiv:1807.07075 [hep-th].
- Shira Chapman, Jens Eisert, Lucas Hackl, Michal P. Heller, Ro Jefferson, Hugo Marrochio, Robert C. Myers: "Complexity and entanglement for thermofield double states", SciPost Phys. 6, 034 (2019), DOI: 10.21468/SciPostPhys.6.3.034 , arXiv:1810.05151 [hep-th].
- Hugo A. Camargo, Michal P. Heller, Ro Jefferson, Johannes Knaute: "Path integral optimization as circuit complexity", Phys. Rev. lett. 123, 011601 (2019), DOI:10.1103/PhysRevLett.123.011601, arXiv:1904.02713 [hep-th].
- Mario Flory, Michal P. Heller: "Geometry of Complexity in Conformal Field Theory", Phys. Rev. Research 2, 043438 (2020), DOI: 10.1103/PhysRevResearch.2.043438, arXiv:2005.02415 [hep-th].
- Mario Flory, Michal P. Heller: "Conformal field theory complexity from Euler-Arnold equations", JHEP 12 (2020) 091, DOI:10.1007/JHEP12(2020)091, arXiv:2007.11555 [hep-th].
- Hugo A. Camargo, Lucas Hackl, Michal P. Heller, Alexander Jahn, Tadashi Takayanagi, Bennet Windt: "Entanglement and Complexity of Purification in (1+1)-dimensional free Conformal Field Theories", (2020), arXiv: 2009.11811 [hep-th].
- A. Ramesh Chandra, Jan de Boer, Mario Flory, Michal P. Heller, Sergio Hörtner, Andrew Rolph: "Spacetime as a quantum circuit", (2021), arXiv:2101.01185 [hep-th].
- P. Fries, I. A. Reyes, "Entanglement Spectrum of a Chiral Fermion on the Torus", Phys. Rev. Lett., vol 123, no. 21, p.211603, 2019. arXiv:1905.05768.
- P. Fries, I. A. Reyes, "Entanglement and relative entropy of a chiral fermion on the torus", Phys. Rev.D 100 (2019) 10, 105015. arXiv:1906.02207
- J. Erdmenger, P. Fries, I. A. Reyes, C. P. Simon, "Resolving modular flow with free fermions", JHEP 12 (2020) 126. arXiv: 2008.07532.
- H. Z. Chen, R. C. Myers, D. Neuenfeld, I. A. Reyes, J. Sandor, "Quantum Extremal Islands Made Easy, Part I: Entanglement on the Brane", JHEP 10 (2020) 166, arXiv: 2006.04851 [hep-th]
- H. Z. Chen, R. C. Myers, D. Neuenfeld, I. A. Reyes, J. Sandor, "Quantum Extremal Islands Made Easy, Part II: Black Holes on the Brane", JHEP 12 (2020) 025, arXiv: 2010.00018 [hep-th]
- W. Florkowski, M. P. Heller, M. Spalinski, Rep. Prog. Phys. 81, 4 (2017), arXiv:1707.02282.
- M.C. Bañuls, M.P. Heller, K. Jansen, J. Knaute, V. Svensson, Phys. Rev. Research 2, 033301 (2020); https://arxiv.org/abs/1912.08836
- Heller, M. P., Jefferson, R., Spaliński, M., & Svensson, V. (2020). Hydrodynamic attractors in phase space. Phys.Rev.Lett, 125(13). arXiv: 2003.07368 [hep-th]
- Heller, M. P., Serantes, A., Spaliński, M., Svensson, V., & Withers, B. (2020). Transseries for causal diffusive systems. arXiv:2011.13864.