About

Understanding strongly correlated systems has been a significant challenge in theoretical physics. However, as computational capabilities continue to improve with the dissemination of new or improved methods, numerical analysis is becoming increasingly important. These days, numerical methods have played a crucial role in theoretical physics, and they enable us to go beyond perturbative analysis and investigate strongly correlated systems. Due to the exponential growth of the Hilbert space, solving a many-body Hamiltonian is known to be notoriously tricky. When it comes to the gapless quantum system in which the low-lying excitations become crucial in understanding the system, naive numerical approaches such as the exact diagonalization are often not capable of correctly capturing the physics. For example, for non-Fermi liquid phases where the conventional Landau Fermi liquid picture breaks down, one has to develop an unbiased numerical method such as quantum Monte Carlo to predict the physical properties of the systems correctly. When the underlying Hamiltonian is sign-problem free, the required computational resource for implementing quantum Monte Carlo scales only polynomially in the system size instead of the exponential scaling of the exact diagonalization.

Quantum phase transition in strongly interacting many-body quantum systems is another example where numerical approaches become powerful. In particular, quantum phase transitions between unconventional phases such as topological phases and non-Fermi liquids are examples where numerical methods become essential since known theoretical methods such as mean-field theory often wholly fail. In one dimension, the density matrix renormalization group (DMRG) method provides a universal tool for computing the critical properties associated with quantum phase transitions. While one often employs cylindrical geometry to understand gapped quantum systems in two dimensions using the DMRG, care must be taken to apply the DMRG to gapless systems, including quantum critical points. Other numerical methods such as quantum Monte Carlo or projected entangled pair states (PEPS) are often more helpful than the DMRG. Numerical analysis of matrix models and AdS/CFT correspondence has shed light on non-perturbative studies of quantum gravity and strongly correlated systems. Much progress in understanding the quantum nature of spacetime has been made via quantum Monte Carlo simulations of matrix models such as IKKT or BFSS models. AdS/CFT correspondence provides a fruitful arena to investigate quantum gravity, strongly coupled systems, and quantum information theory with numerical methods. The numerical techniques have been extensively used in reconstructing spacetime and emergent gravity via holographic renormalization group, multi-scale entanglement renormalization ansatz (MERA), tensor networks, and deep learning to see how spacetime is reconstructed from gauge theory data. The SYK model has also provided a promising way for the numerical analysis of quantum black holes, including phase transition and the black hole information paradox. Machine learning is a newly-developing computational technique in theoretical physics. Although machine learning bears incredible potential, efforts to fully utilize the potential in physics are still in their early stages. It is crucial to apply machine learning to physics to build and develop theoretical foundations of machine learning, such as the formal concepts of information, intelligence, and interpretability. In addition, the theoretical connection of deep learning with the renormalization group and tensor networks is a significant challenge. This program will also cover applications in the design of quantum computers and devices, such as neural networks for decoding, quantum error correction, and tomography.

The program aims to bring together different communities of theoretical physicists working on numerical methods to investigate those types of questions. Cross-fertilizing ideas and finding common ground should inspire new ways of thinking about these problems and stimulate more rapid progress.

Location

APCTP, Pohang, Korea + online (Zoom)

Program

May 16 (Mon) - 20 (Fri), 2022

The schedule below is in the Korean Standard Time (KST = UTC+9).

Invited speakers

• Fabien Alet (CNRS) (online)

• David Berenstein (UC Santa Barbara)

• Pietro Brighi (IST Austria)

• Snir Gazit (Hebrew Univ.) (online)

• Ryo Hanai (APCTP) (online)

• Masanori Hanada (Univ. of Surrey) (online)

• Masazumi Honda (YITP, Kyoto Univ.) (online)

• Anosh Joseph (IISER Mohali)

• Raghav Jha (Perimeter Inst.) (online)

• David Luitz (Univ. of Bonn) (online)

• Robert de Mello Koch (WITS) (online)

• Frank Pollmann (TUM) (online)

• Rak-Kyeong Seong (UNIST) (online)

• David Schaich (Univ. of Liverpool) (online)

• Piotr Sierant (ICFO) (online)

• Kazuki Yamamoto (Kyoto Univ.) (online)

Organizers

• Anosh Joseph (IISER Mohali)

• Byungmin Kang (KIAS)

• Dario Rosa (IBS)

• Masaki Tezuka (Kyoto University)

• Junggi Yoon (APCTP)