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Program
| 8/5 | 8/6 | 8/7 | 8/8 | ||
| Mon | Thu | Wed | Thu | ||
| Venue | Rm. SC158, 1F, Science Building III, NYCU | ||||
| 08:30-09:00 | Registration | ||||
| Chair | Chang-Tse Hsieh | Chia-Min Chung | Chung-Hou Chung | Shin-Ming Huang | |
| 09:00-10:15 | Chung-Hou Chung | Ian McCulloch | Sungsik Lee (online) |
Tsung-Han Lee | |
| 10:15-10:45 | Coffee Break | ||||
| 10:45-12:00 | Akira Furusaki | Ying-Jer Kao | Hoa Nghiem (online) |
Chisa Hotta | |
| 12:00-14:00 | Lunch | ||||
| Chair | Po-Yao Chang | Yi-Ping Huang | Pochung Chen | Chien-Te Wu | |
| 14:00-15:15 | Yu-Te Hsu | Hiroshi Shinaoka (online) |
Jan von Delft (online) |
Atsushi Fujimori | |
| 15:15-15:45 | Coffee Break | ||||
| 15:45-17:00 | Chia-Min Chung | Chung-Hou Chung | Yi-Hsien Du | Tsung-Han Lee | |
| 17:00-18:00 | Discussion | ||||
Youtube：8/5 https://youtu.be/mmvtRp0InHU
8/6 https://youtu.be/Ajo5UdUZTU4
8/7 https://youtu.be/g1L0Jjlw-oc
8/8 https://youtu.be/_Ymc-vYGCwo
Slides：1YtreQHZ1HSN2O0qN4DaGAjbDEVFNKPt4
| 5th August | |
| Time | Title/Speaker |
| 08:30-09:00 | Registration |
| 09:00-10:15 | Title: Introduction to Renormalization Group approach to condensed matter systems Prof. Chung-Hou Chung (NYCU) Abstract: In this talk, I will give an overview of the Renormalization Group (RG) approach to many-body condensed matter systems. I will focus on how RG approach helps to theoretically study phase transitions (both classical and quantum phase transitions) and critical phenomena that are experimentally observed in various condensed matter systems. Specific examples of RG analysis in magnetic materials (both classical and quantum magnets) and strongly correlated unconventional superconductors (high-Tc cuprates) are provided. |
| 10:15-10:45 | Coffee break |
| 10:45-12:00 | Title: Bosonization of 1D interacting fermions and quantum spin chains. Prof. Akira Furusaki (RIKEN) Abstract: I will give an introduction to bosonization of one-dimensional interacting fermions and its application to the spin-1/2 XXZ model. I will then discuss the phase diagram of the frustrated J1-J2 XYZ model and quantum phase transitions between the dimer and Neel ordered phases [1]. [1] C. Mudry, A. Furusaki, T. Morimoto, and T. Hikihara, Phys. Rev. B 99, 205153 (2019). |
| 12:00-14:00 | Lunch |
| 14:00-15:15 |
Title: Charge transport in superconducting cuprates and nickelates — beyond the standard Boltzmann framework. Prof. Yu-Te Hsu (NTHU) Abstract: The resistivity of materials is often the first quantity to be measured yet the last to be understood. The current standard theory of electronic transport is the Boltzmann transport theory, which is based on finding the distribution function of the electronic liquid under external perturbations. Within the Boltzmann framework, the electronic liquid relaxes back to its equilibrium state from the non-equilibrium state after perturbation of electro-magnetic field or thermal gradient via scattering mechanisms. In the high-temperature superconducting copper oxides (i.e. high-Tc cuprates), several transport properties in the so-called ‘strange metal’ regime exhibit anomalous behavior that has been a subject of intense investigation. It has recently been demonstrated that the Boltzmann framework can describe the resistivity [1], magneto-resistance [2], and thermoelectric response [3] remarkably well in the archetypical high-Tc cuprates La2-xSrxCuO4. At the same time, magneto-transport studies on Bi2Sr2CuO6+δ and Tl2Ba2CuO6+δ found that in these compounds the charge transport cannot be described by the Boltzmann framework, prompting a debate on whether the charge-carrying entities in the cuprate strange metals can be described as coherent fermionic quasiparticles. In the first part of this tutorial, I will sketch the strange-metal phenomenology in the high-Tc cuprates, highlight the central concepts of the Boltzmann transport theory, and its recent success in accounting for the transport properties of the cuprate strange metal. In the second part, I will highlight cases in which the Boltzmann theory fails to capture the experimental results on a qualitative level, including magnetotransistance in overdoped Bi2201 and Tl2201 and optimally doped infinite-layer nickelates, and magneto-thermopower in overdoped Bi2201. Reference [1] Grissonnanche et al., Nature 595, 667-672 (2021) [2] Ataei et al., Nature Physics 18, 1420-1424 (2022) [3] Gourgout et al., PRX 12, 011037 (2022) [4] Ayres et al., Nature 595, 661-666 (2021) |
| 15:15-15:45 | Coffee break: Afternoon break |
| 15:45-17:00 | Tutorial: MPS/MPO/DMRG Prof. Chia-Min Chung (NSYSU) |
| 17:00-18:00 | |
| 6th August | |
| Time | Title/Speaker |
| 08:30-09:00 | Registration |
| 09:00-10:15 |
Title: Real and imaginary time evolution for matrix product states Prof. Ian McCulloch (NTHU) Abstract: I will give an overview/tutorial on applications and methods for time evolution in matrix product states (MPS). Applications include calculating low-lying excitations and spectral functions, quantum quenches, dynamical quantum phase transitions, evolution of wave packets, and imaginary time evolution for constructing thermal density matrices. I will briefly summarize the main algorithms, including TEBD, TDVP, Krylov algorithms, and MPO approximations of the time evolution operator. |
| 10:15-10:45 | Coffee break: Morning break |
| 10:45-12:00 |
Title: Quantum Spin liquids. Prof. Ying-Jer Kao (NTU) Abstract: In this talk, I will give an introduction on quantum spin liquids (QSL). QSL are characterized by long-range quantum entanglement and their highly entangled nature gives unique physical aspects, such as non-local excitations, topological properties, and more. I will discuss theoretical and numerical methods which are used in the study of quantum spin liquids. Finally, I will mention candidate experimental systems to search QSL in nature. |
| 12:00-14:00 | Lunch |
| 14:00-15:15 |
Title: Exploiting hidden low-rank structures in quantum field theories. Prof. Hiroshi Shinaoka (Saitama University) (online) Abstract: Tensor networks are a powerful tool for compressing wave functions and density matrices of quantum systems in physics. Recent developments have shown that tensor network techniques can efficiently compress many functions beyond these traditional objects. Notable examples include the solutions to turbulence in Navier–Stokes equations [1] and the computation of Feynman diagrams [2,3]. These advancements have heralded a new era in the use of tensor networks for expediting the resolution of various complex equations in physics. This talk will provide an overview of our work utilizing tensor networks for computations based on quantum field theories. First, we will introduce the Quantics/quantized Tensor Train (QTT) representation [3,4] for compressing the space-time dependence of correlation functions in quantum systems [5], leveraging inherent length-scale separation for efficient representation. Second, we will present a robust tool named “Quantics Tensor Cross Interpolation” [6], which learns a quantics low-rank representation of a given function. Applications include the computation of Brillouin zone integrals [6] and integration of complex self-energy Feynman diagrams for multiorbital electron-phonon impurity models [7]. Finally, we will introduce new algorithms [8] and open-source libraries [9] for tensor cross interpolation. [1] N. Gourianov et al., Nat. Comput. Sci. 2, 30 (2022). [2] Y. N. Fernandez et al., PRX 12, 041018 (2022). [3] I. V. Oseledets, Dokl. Math. 80, 653 (2009). [4] B. N. Khoromskij, Constr. Approx. 34, 257 (2011). [5] H. Shinaoka et al., PRX 13, 021015 (2023). [6] M. K. Ritter, Y. N. Fernández, M. Wallerberger, J. von Delft, H. Shinaoka and X. Waintal, PRL 132, 056501 (2024). [7] H. Ishida, N. Okada, S. Hoshino, H. Shinaoka, arXiv:2405.06440v2. [8] Y. N. Fernández, M. K. Ritter, M. Jeannin, J.-W. Li, T. Kloss, T. Louvet, S. Terasaki, O. Parcollet, J. von Delft, H. Shinaoka and X. Waintal, arXiv:2407.02454v1 [9] https://tensor4all.org |
| 15:15-15:45 | Coffee break: Afternoon break |
| 15:45-17:00 | Tutorial: RG Prof. Chung-Hou Chung |
| 7th August | |
| Time | Title/Speaker |
| 08:30-09:00 | Registration |
| 09:00-10:15 | Title: Non-Fermi liquid theories. Prof. Sungsik Lee (PITP) (online) https://arxiv.org/abs/1703.08172 https://arxiv.org/abs/2208.00730 https://arxiv.org/abs/2405.09450 I will try to cover low-energy effective field theories for non-Fermi liquids with emphasis on the recent development of non-perturbative approaches and field-theoretic functional renormalization group formalism needed to take into account UV/IR mixing. |
| 10:15-10:45 | Coffee break: Morning break |
| 10:45-12:00 |
Title: Numerical renormaliztion group method for quantum impurity systems from basis to recent developments. Prof. Hoa Nghiem (Phenikaa University) Abstract: In this lecture, I will introduce the general idea of the renormalization group method for a quantum system and provide the detailed setup of Wilson's numerical renormalization group calculation to solve a quantum impurity problem [1]. For recent developments, I will present the construction of a complete basis set collected from the numerical renormalization group method, which enables the establishment of a time-dependent version of the numerical renormalization group method [2]. The application to investigate both the thermodynamics and transient dynamics of the Ohmic two-state system will be shown by exploiting the equivalence of this model to the interacting resonant level model [3]. [1] R. Bulla, T. A. Costi, and T. Pruschke. Rev. Mod. Phys. 80, 395 (2008). [2] H. T. M Nghiem, T. A. Costi. Physical Review B 89, 075118 (2014). [3] H. T. M. Nghiem, D. M. Kennes, C. Klöckner, V. Meden, and T. A. Costi. Phys. Rev. B 93, 165130 (2016). |
| 12:00-14:00 | Lunch |
| 14:00-15:15 | Title: The physics of quantum impurity models. Prof. Jan von Delft (LMU) (Online) Abstract: I will give an introductory overview of the physics of quantum impurity models and the concept of spin screening. I will introduce two paradigmatic models describing spin screening: the single-impurity Anderson model and the Kondo model; explain why a perturbative treatment fails at low temperatures; review Wilson's numerical renormalization group (NRG) approach for reaching low temperature; discuss various physical quantities exhibiting signatures of spin screening; and discuss a model that does not show full spin screening---the two-channel Kondo model. Finally, I will discuss how the physics of spin screening manifests itself when treating the Hubbard model using dynamical mean field theory (DMFT). |
| 15:15-15:45 | Coffee break: Afternoon break |
| 15:45-17:00 | Tutorial: Nonlinear Bosonization of (Non-)Fermi Liquids Fermi liquid theory is a cornerstone of condensed matter physics. I will show how to formulate Fermi liquid theory as an effective field theory. In this approach, the space of low-energy states of a Fermi liquid is identified with a coadjoint orbit of the group of canonical transformations. The method naturally leads to a nonlinear bosonized description of the Fermi liquid with nonlinear corrections fixed by the geometry of the Fermi surface. I will present that the resulting local effective field theory captures both linear and nonlinear effects in Landau’s Fermi liquid theory. The approach can be extended to encompass non-Fermi liquids, which correspond to strongly interacting fixed points obtained by deforming Fermi liquids with relevant interactions. I will also discuss how noncommutativity can be captured in the coherent state path integral approach. Dr. Yi-Hsien Du |
| 8th August | |
| Time | Title/Speaker |
| 08:30-09:00 | Registration |
| 09:00-10:15 | Title: Introduction to Dynamical Mean-Field Theory and Beyond. Prof. Tsung-Han Lee (NCCU) Abstract: In this lecture, I will introduce dynamical mean-field theory (DMFT) and its extensions beyond DMFT [1-5]. I will begin by providing an overview of the relationship between classical mean-field theory and quantum dynamical mean-field theory. Following this, I will review the theoretical foundation of DMFT and introduce the concept of infinite dimensions, where DMFT becomes an exact quantum theory [1]. I will then present the DMFT self-consistent equations and the algorithm for solving them. Next, I will chronologically review significant breakthroughs in DMFT applications and extensions. This includes early applications to the Hubbard model [1], the cluster-DMFT extensions for d-wave superconductors [2], the density functional theory plus DMFT applications to correlated materials [3], the non-equilibrium DMFT formalism [4], the diagrammatic DMFT extensions [5], and finally, the connection between DMFT and other similar quantum embedding approaches [6]. [1] Antoine Georges, Gabriel Kotliar, Werner Krauth, and Marcelo J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996). [2] Thomas Maier, Mark Jarrell, Thomas Pruschke, and Matthias H. Hettler, Rev. Mod. Phys. 77, 1027 (2005). [3] G. Kotliar, S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet, and C. A. Marianetti, Rev. Mod. Phys. 78, 865 (2006). [4] Hideo Aoki, Naoto Tsuji, Martin Eckstein, Marcus Kollar, Takashi Oka, and Philipp Werner, Rev. Mod. Phys. 86, 779 (2014). [5] G. Rohringer, H. Hafermann, A. Toschi, A. A. Katanin, A. E. Antipov, M. I. Katsnelson, A. I. Lichtenstein, A. N. Rubtsov, and K. Held, Rev. Mod. Phys. 90, 025003 (2018). [6] Thomas Ayral, Tsung-Han Lee, and Gabriel Kotliar, Phys. Rev. B 96, 235139 (2017). |
| 10:15-10:45 | Coffee break: Morning break |
| 10:45-12:00 | Title: Toward finding an optimal local density matrix in quantum many-body systems. Prof. Chisa Hotta (UTokyo) Abstract: The quantum many-body state we want to obtain is the one that generates the physical quantities accurately enough to mimic the ones in the thermodynamic limit in the equilibrium. Such quantity is often local, e.g. energy or magnetization densities, which means that we need to obtain a good local density matrix to evaluate them. Suppose that we have an isolated quantum system, divided into subsystem A and the rest of the system B, where $A \ll B$, and we have a quantum state $\Psi$, which is the exact ground state of the total system. The full information on A is stored in the local density matrix $\rho_A=Tr_B (|\Psi\rangle\langle\Psi|)$. However, if we could only find an approximate $\Psi_{tr}$, the question is, how can we obtain them within a good accuracy? The density matrix embedding theory (DMET) proposed by Garnet Chan's group[1,2] is one of such trials, finding a proper one-body potential that generates a good trial wave function whose local density matrix on A mimics that of the exact ones. However, the optimization of this method is not variational, which makes it difficult to convince ourselves whether the solutions we obtained are really optimal. While the big advantage of DMET over other cluster methods is that it does not suffer cluster-shape/side effects, can keep long-range correlations accurately, and can even reproduce the exact entanglement spectrum which is the fingerprint of the quantum many body state [3,4]. This is because DMET does not really cut out physically the cluster Hamiltonian. I will provide some examples and experiences in working on this method [3,4]. [1] G. Knizia and G. K.-L. Chan, Phys. Rev. Lett. 109, 186404 (2012). [2] Q. Chen, G. H. Booth, S. Sharma, G. Knizia, and G. K.-L. Chan, Phys. Rev. B 89, 165134 (2014). [3] X. Plat and C. Hotta, Phys. Rev. B 102, 140410 (2020). [4] M. Kawano and C. Hotta, Phys. Rev. B 102, 235111 (2020). |
| 12:00-14:00 | Lunch |
| 14:00-15:15 | Title: ARPES and RIXS studies of cuprate superconductors. Prof. Atsushi Fujimori (University of Tokyo & National Tsing Hua University) Abstract: In this lecture, first I will introduce the angle-resolved photoemission spectroscopy (ARPES) and resonant inelastic x-ray scattering (RIXS) techniques and explain what one can learn about the charge and spin states of correlated electrons and their excitation using these techniques. Then, I will summarize unresolved problems in high-Tc cuprates such as the origins of the pseudogap, charge-density wave (CDW) order, nematic order, and quantum critical points (QCP), and will show how these problems can be tackled using ARPES and RIXS. In particular, indications of electron fractionalization [1] in the high-temperature, low-doping region of the pseudogap phase are demonstrated by ARPES [2] and RIXS [3]. As the temperature is lowered, the pseudogap crossovers to the d-wave-like gap [4]. In the low-temperature, overdoped region near QCP, characteristic CDW fluctuations intertwined with superconductivity are observed by RIXS [5]. [1] S. Sakai, A. Sacuto, A. Georges, M. Imada et al., Phys. Rev. Lett. 111, 107001 (2013). [2] M. Horio, S. Sakai, K. Koshiishi, Y. Nonaka, H. Suzuki, J. Xu, M. Hashimoto, D. Lu, Z.-X. Shen, T. Ohgi, T. Konno, T. Adachi, Y. Koike, M. Imada, A. Fujimori: arXiv:1801.04247; under review. [3] A. Singh, H. Y. Huang, J. D. Xie, J. Okamoto, C. T. Chen, T. Watanabe, A. Fujimori, M. Imada, and D. J. Huang: Nat. Commun. 13, 7906 (2022). [4] S. Ideta, S. Uchida, T. Watanabe, C. Y. Mou, T. Yoshida, T. K. Lee, A.Fujimori et al., in preparation. [5] H. Y. Huang, A. Singh, C. Y. Mou, S. Johnston, A. F. Kemper, J. van den Brink, P. J. Chen, T. K. Lee, J. Okamoto, Y. Y. Chu, J. H. Li, S. Komiya, A. C. Komarek, A. Fujimori, C. T. Chen, and D. J. Huang: Phys. Rev. X 11, 041038 (2021). |
| 15:15-15:45 | Coffee break: Afternoon break |
| 15:45-17:00 | Tutorial: DMFT Prof. Tsung-Han Lee |
