2024.9.12: Ángel L. Corps氏（Instituto de Estructura de la Materia, IEM-CSIC, Madrid, Spain）
日時：9月12日（木） 16:00-18:00
場所：オンライン
Title: NON-EQUILIBRIUM DYNAMICAL EFFECTS OF EXCITED-STATE QUANTUM PHASE TRANSITIONS
Abstract:
In recent years we have witnessed great developments in our understanding of non-equilibrium dynamical phases in many-body quantum systems. Excited-state quantum phase transitions extend the notion of the traditional ground-state criticality to high-lying eigenstates of a quantum systems. They denote some forms of non-analytic behavior at certain critical energy densities, entailing important effects that can be observed in the dynamical evolution of closed quantum systems. In this talk I will review some recent results linking dynamical phase transitions and excited-state quantum phase transitions. In particular I will focus on some extensions of the standard tools of the eigenstate thermalization hypothesis to describe non-equilibrium order parameters in fully-connected and strongly correlated models. I will also explain how non-analytical times in survival probabilities are precluded from taking place in symmetry-breaking phases of these models.
REFERENCES
[1] A. L. Corps and A. Relaño, Dynamical and excited-state quantum phase transitions in collective systems, Phys. Rev. B 106, 024311 (2022).
[2] A. L. Corps and A. Relaño, Theory of dynamical phase transitions in systems with symmetry-breaking eigenstates, Physical Review Letters 130, 100402 (2023).
[3] A. L. Corps, P. Stránský and P. Cejnar, Mechanism of dynamical phase transiitons: The complex time survival amplitude, Phys. Rev. B 107, 094307 (2023).
[4] A. L. Corps, J. Dukelsky and A. Relaño, Constants of motion characterizing continuous symmetry-broken phases, Phys. Rev. E 109, 064102 (2024).
[5] A. L. Corps and A. Relaño, General theory for discrete symmetry-breaking equilibrium states, arXiv:2303.18020.
[6] A. L. Corps and A. Relaño, Constant of motion identifying excited-state quantum phases, Phys. Rev. Lett. 127, 130602 (2021).
[7] A. L. Corps, A. Relaño and J. C. Halimeh, Unifying Finite-Temperature Dynamical and Excited-State Quantum Phase Transitions, PRResearch (in press).
2024.7.11: Sparsh Gupta氏（International Centre for Theoretical Sciences）
日時：7月11日（木） 15:00-16:30 (Sorry for the sudden change of the schedule)
場所：理化学研究所 和光キャンパス 研究本館 4階 435-437
Title: Quantum jumps in driven-dissipative disordered many-body systems
Abstract:
We discuss how quantum jumps affect localized regimes in driven-dissipative disordered many-body systems featuring a localization transition. We introduce a deformation of the Lindblad master equation that interpolates between the standard Lindblad and the no-jump non-Hermitian dynamics of open quantum systems. As a platform, we use a disordered chain of hard-core bosons with nearest-neighbor interactions and subject to incoherent drive and dissipation at alternate sites. We probe both the statistics of complex eigenvalues of the deformed Liouvillian and dynamical observables of physical relevance. We show that reducing the number of quantum jumps, achievable through realistic post-selection protocols, can promote the emergence of the localized phase. Our findings are based on exact diagonalization and time-dependent matrix-product state techniques.
2024.4.17: Budhaditya Bhattacharjee氏（Institute for Basic Sciences）
日時：4月17日（水） 14:30-16:00
場所：理化学研究所 和光キャンパス 研究本館 4階 445-447
Title: Operator Growth in Open Quantum Systems : Perspectives from Lindbladian SYK via Krylov Complexity
Abstract:
In this talk, I will discuss some general features of operator growth in open quantum systems governed by Lindbladian evolution. I will introduce two orthonormalization techniques, namely Arnoldi and BiLanczos algorithms, using which I will capture the evolution of the operator in an appropriate basis. In these bases, many features of the evolution of operators (including relevant time scales) will emerge naturally. I will motivate these bases choices from results in closed quantum systems. I will utilize the paradigmatic setup of the Sachdev-Ye-Kitaev model to describe the system and environment, and closely related system-environment interaction. I will present numerical results in this setup and derive some analytical results. I will also discuss the nature of correlation function and spectral function in such open quantum systems. Then I will discuss features of a large class of probes (that do not rely on the same choice of basis) in such systems. I will end by mentioning implications of these results in other areas of research, and some open questions/future directions.
[1] Operator dynamics in Lindbladian SYK: a Krylov complexity perspective, JHEP 01 (2024) 094
[2] Operator growth in open quantum systems: lessons from the dissipative SYK, JHEP 03 (2023) 054
2022.9.8: 田中智啓氏（東工大）
日時：9月8日（木） 14:00-16:00
場所：オンライン（Zoom）
Title: Transport coefficients of Lieb-Liniger model and related models
Abstract:
Lieb-Liniger model is a one-dimensional Bose gas with a two-body contact interaction. This model is known to be integrable and has divergent transport coefficients. Additionally, when we experimentally realize a one-dimensional Bose gas by confining a three-dimensional Bose gas, a three-body interaction appears to break the integrability. These facts motivate us to study transport coefficients of the one-dimensional Bose gas with two-body and three-body interactions theoretically. Furthermore, the Lieb-Liniger model is known to be the dual of the Cheon-Shigehara model, where the thermodynamic properties of one of the models at weak coupling coincide with that of the other at strong coupling. It is not well studied whether the duality extends beyond the thermodynamics to the correlation functions, so finding a transport coefficient that satisfies the duality is significant.
In this seminar, we discuss two topics related to the above. First, we calculate the thermal conductivity of the one-dimensional Bose gas with two-body and three-body interactions perturbatively. Since there are a series of diagrams that are naively higher order in the perturbation but become the lowest order due to the pinch singularities, we have to sum up all contributions from such diagrams even though we evaluate the Kubo formula in the lowest order. Second, we apply Girardeau’s Bose-Fermi mapping to the Kubo formula for the bulk viscosity, showing that the bulk viscosities of the two models are identical at the same scattering length. We also compute their bulk viscosities perturbatively in the weak-coupling limit, which via the duality serve as those of the two models in the strong-coupling limit.
[1] T.Tanaka and Y.Nishida, Thermal conductivity of a weakly interacting Bose gas by quasi-one dimensionality, arXiv preprint arXiv:2203.04936 (2022).
[2] T.Tanaka and Y.Nishida, Bulk viscosity of dual Bose and Fermi gases in one dimension, arXiv preprint arXiv:2206.07848 (2022).
2021.5.26: 鈴木遼太郎氏（阪大→ベルリン自由大学）
日時：5月26日（水） 16:00-17:00
場所：オンライン（Zoom） 参加登録は前日までに、右よりお願いします forms.gle/Z9igaNko3nstaDes5
タイトル：1次元及び2次元デュアルユニタリ量子回路の計算能力
アブストラクト：
量子コンピュータは古典コンピュータを凌駕する計算能力を持つと信じられている。そのため量子コンピュータを古典コンピュータで効率よくシミュレートすることが、一般には不可能だと考えられている。ところが、いくつかの量子回路は量子特有の相関を生み出すにもかかわらず、古典コンピュータで効率よくシミュレート出来る[1,2]。古典シミュレート可能な量子回路を新たに構築することは、どの様な制限の下で量子特有の計算能力を失うか、またどの様な要素が量子加速に必要かを調べる上で重要である。一方で最近、デュアルユニタリ量子回路と呼ばれる量子回路が非平衡多体系の可解模型として注目を集めており、熱力学極限における局所物理量の期待値や相関関数が厳密に求められている[3]。
本セミナーでは、1次元及び2次元デュアルユニタリ量子回路を量子計算モデルと見なし、その計算能力について調べた研究結果を発表する[4]。具体的には、我々はデュアルユニタリ量子回路の局所物理量の期待値を計算出力とするモデルについて考えた。その結果、回路深さが浅い時（量子ビット数程度まで）は、局所物理量の期待値が古典シミュレート可能になる一方で、回路深さが十分深い時はこの量子回路が万能量子計算可能になる事が分かった。それに加えて、デュアルユニタリ量子回路全体の出力を古典コンピュータによりサンプルすることは、計算量的仮定の下で困難である事がわかった。
本発表では、量子計算や量子回路モデルの基礎知識から話す予定である。
[1] D. Gottesman, Stabilizer codes and quantum error correction, PhD thesis, California Institute of Technology (1997).
[2] L. G. Valiant, Quantum circuits that can be simulated classically in polynomial time, SIAM Journal on Computing 31, 1229 (2002).
[3] L. Piroli, B. Bertini, J. I. Cirac, and T. Prosen, Exact dynamics in dual-unitary quantum circuits, Physical Review B 101, 094304 (2020).
[4] R. Suzuki , K. Mitarai, and K. Fujii, Computational power of one-and two-dimensional dual-unitary quantum circuits, arXiv preprint arXiv:2103.09211 (2021).
研究チームのセミナーでの紹介論文
FY2025
*A. Schnell et al., "Is there a Floquet Lindbladian?" Phys. Rev. B 101, 100301 (2020). [Yoshida]
M. M. Wolf et al., "Assessing Non-Markovian Quantum Dynamics," Phys. Rev. Lett. 101, 150402 (2008). [Yoshida]
*R. H. Dicke, "Coherence in Spontaneous Radiation Processes," Phys. Rev. 93, 99 (1954). [Yoshimura]
A. Angerer et al., "Superradiant emission from colour centres in diamond," Nature Physics 14, 1168–1172 (2018). [Yoshimura]
*S. J. Garratt and J. T. Chalker, "Local Pairing of Feynman Histories in Many-Body Floquet Models," Phys. Rev. X 11, 021051 (2021). [Oshima]
A. Chan et al., "Spectral Statistics in Spatially Extended Chaotic Quantum Many-Body Systems," Phys. Rev. Lett. 121, 060601 (2018). [Oshima]
*S. Sudevan et al., "Multipartite entanglement and quantum error identification in 𝐷-dimensional cluster states," Phys. Rev. A 108, 022426 (2023). [Chiba]
*A. Bastianello et al., "Fragmentation and Emergent Integrable Transport in the Weakly Tilted Ising Chain," Phys. Rev. Lett. 128, 196601 (2022). [Sekino]
U. Borla et al., "Confined Phases of One-Dimensional Spinless Fermions Coupled to 𝑍2 Gauge Theory," Phys. Rev. Lett. 124, 120503 (2020). [Sekino]
ZC. Yang et al., "Hilbert-Space Fragmentation from Strict Confinement," Phys. Rev. Lett. 124, 207602 (2020). [Sekino]
*L. Leone and L. Bittel, "Stabilizer entropies are monotones for magic-state resource theory," Phys. Rev. A 110, L040403 (2024). [Maity]
*K. C. Smith et al., "Constant-Depth Preparation of Matrix Product States with Adaptive Quantum Circuits," PRX Quantum 5, 030344 (2024). [Hamazaki]
FY2024
*P. Sala et al., "Spontaneous Strong Symmetry Breaking in Open Systems: Purification Perspective," arXiv:2405.02402 (2024). [Oshima]
*J. R. McClean et al., "Barren plateaus in quantum neural network training landscapes," Nature Communications volume 9, Article number: 4812 (2018). [Sugimoto]
*A. Bakshi et al., "High-Temperature Gibbs States are Unentangled and Efficiently Preparable," arXiv:2403.16850 (2024). [Chiba]
*D. T. Stephen et al., "Ergodicity Breaking Provably Robust to Arbitrary Perturbations," Phys. Rev. Lett. 132, 040401 (2024). [Sekino]
*L. Leone et al., "Stabilizer Rényi Entropy," Phys. Rev. Lett. 128, 050402 (2022). [Maity]
*J. Yang et al., "Variational Principle for Optimal Quantum Controls in Quantum Metrology," Phys. Rev. Lett. 128, 160505 (2022). [Hamazaki]
S. Pang and A. N. Jordan, "Optimal adaptive control for quantum metrology with time-dependent Hamiltonians," Nature Communications volume 8, Article number: 14695 (2017). [Hamazaki]
FY2022
*H-Y. Huang et al., "Predicting many properties of a quantum system from very few measurements," Nature Physics volume 16, pages 1050–1057 (2020). [Hamazaki]
*S. Aaronson and A. Arkhipov, "The computational complexity of linear optics," STOC '11: Proceedings of the forty-third annual ACM symposium on Theory of computing (2011). [Mochizuki]
*D. E. Parker et al., "A Universal Operator Growth Hypothesis," Phys. Rev. X 9, 041017 (2019). [Maity]