Research
Research directions and projects:
Entanglement in Many Body states
Entanglement entropy and entanglement spectrum of many-body states and its manifestation in the statistics of measurable quantities, with a special focus on states which are of interest in condensed matter, such as topological insulators and quantum Hall states.
More recently I have been working on dynamical aspects: entanglement generation and how to form interesting quantum dynamics using measurements.
Selected papers:
I. Klich, D. Vaman and G. Wong, Entanglement Hamiltonians for chiral fermions, arXiv:1501.00482
G. Wong, I. Klich, L. A. Pando Zayas, D. Vaman, Entanglement Temperature and Entanglement Entropy of Excited States, JHEP 12 (2013) 020
H. Francis Song, C. Flindt, S. Rachel, I. Klich and K. Le-Hur, Entanglement from Charge Statistics: Exact Relations for Many-Body Systems, Phys. Rev. B 83, 161408 (2011)
I. Klich and L. Levitov, Quantum Noise as an Entanglement Meter. Phys. Rev. Lett. 102, 100502 (2009)
D. Gioev and I. Klich, Entanglement entropy of fermions in any dimension and the Widom conjecture. Phys. Rev. Lett. 96, 100503 (2006).
I. Klich, Lower entropy bounds and particle number fluctuations in a Fermi sea. J. Phys. A:Math and General 39 (2006) L85-L92.
Quantum Electromagnetic fluctuations
Quantum electromagnetic fluctuations and light-matter interaction with boundaries through the Casimir effect, a striking phenomenon predicted by quantum theory describing the attraction between mirrors due to zero point fluctuations of the electromagnetic field.
Selected papers:
I Klich, On the entanglement of a quantum field with a dispersive medium, Phys. Rev. Lett. 109, 061601 (2012)
O Kenneth and I Klich, Casimir forces in a T operator approach.Phys. Rev. B 78, 014103 (2008).
O Kenneth and I Klich, Opposites Attract - A Theorem About The Casimir Force. Phys. Rev. Lett. 97, 160401 (2006).
O Kenneth, I Klich, A Mann and M Revzen. Repulsive Casimir forces. Phys. Rev. Let. 89, 033001 (2002)
Israel Klich, Casimir's energy of a conducting sphere and of a dilute dielectric ball. Phys. Rev. D61 (2000) 025004.
Mathematical physics
Birman-Schwinger counting of Andreev states in superconductors, Lieb Robinson bounds and stability of topological phases are recent projects.
Selected papers:
I Klich, A note on the Full Counting Statistics of paired fermions, J. Stat. Mech. (2014) P11006
I Klich , Birman-Schwinger and the number of Andreev states in BCS superconductors, Phys. Rev. B 83, 184505 (2011)
L Fidkowski, T S Jackson and I Klich, Model Characterization of Gapless Edge Modes of Topological Insulators Using Intermediate Brillouin-Zone Functions, Phys. Rev. Lett. 107, 036601 (2011)
I. Premont-Schwarz, A. Hamma, I. Klich, F. Markopoulou-Kalamara, Lieb-Robinson bounds for commutator-bounded operators Physical Review A Vol.81, No.4 (2010)
I Klich, On the stability of topological phases on a lattice Annals of Physics, Volume 325, Issue 10, p. 2120-2131 (2010).
I Klich, Full Counting Statistics: An elementary derivation of Levitov's formula. Invited contribution to "Quantum Noise", edited by Yu. V. Nazarov and Ya. M. Blanter (Kluwer 2003) cond-mat/0209642.
J. E. Avron, S. Bachmann, G. M. Graf and I. Klich, Fredholm determinants and the statistics of charge transport. Comm. Math. Phys. 280, 807–829 (2008).
Magnetism, Frustration and Glassiness
A tiling based proof of exotic entropy scaling in a system exhibiting glassiness due to an interplay of quantum fluctuations and frustration.
Selected papers:
J. Yang, A. M. Samarakoon, S. E. Dissanayake, H. Ueda, I. Klich, K. Iida, D. Pajerowski, N. Butch, Q. Huang, J.R.D. Copley, S.-H. Lee, Spin Jam: a quantum-fluctuation-induced glassy state of a frustrated magnet. Proc. Nat. Acad. Sci. , 10.1073/pnas.1503126112
I. Klich, S.-H. Lee, K. Iida, From frustration to glassiness via quantum fluctuations and random tiling with exotic entropy, Nature Com 5, 3497, 2014.
Highly entangled states , Tensor networks
Random many body states contain high entanglement by some measures. However, typical ground states of quantum Hamiltonians are usually not highly entangled. In spite of that it is possible to construct toy systems with a large ammount of entanglement. Such models have often a geometrical interpretation and associated natural tensor networks structures.
Selected papers:
Novel quantum phase transition from bounded to extensive entanglement, Z Zhang, A Ahmadain, I Klich, Proceedings of the National Academy of Sciences 114 (20), 5142-5146 (2023)
Exact holographic tensor networks for the Motzkin spin chain, RN Alexander, G Evenbly, I Klich, Quantum 5, 546 (2021)
Deformed Fredkin spin chain with extensive entanglement, O Salberger, T Udagawa, Z Zhang, H Katsura, I Klich, V Korepin, Journal of Statistical Mechanics: Theory and Experiment 2017 (6), 063103
Coupled Fredkin and Motzkin chains from quantum six-and nineteen-vertex models, Z Zhang, I Klich, SciPost Physics 15 (2), 044 (2017)
PhD Students:
Current
Biran Khor
Graduated
Matthew Wampler (--> postdoc, SISSA, Triesta)
Zhao Zhang (--> postdoc, SISSA, Triesta)
Amr Ahmadain ( postdoc, Cambridge, UK)
Gabriel Wong (w. Diana Vaman) (--> postdoc, Harvard)
Yifei Shi (--> postdoc, McGill)
Co-authors:
Yosi Avron
David Benjamin
Eugene Demler
John F. Dobson
Joshua Feinberg
Adrian Feiguin
Diana Vaman
Leopoldo AP Zayas
Yue Zou
Oded Kenneth
Kun-Woo Kim
Christian Flindt
Lucasz Fidkowski
Timothy Gould
Dimitri Gioev
Gian-Michele Graf
Aliosca Hamma
Kazuki Iida
Thomas S. Jackson
Andrew J. James
Hosho Katsura
Jonathan Keeling
Vladimir Korepin
Karyn Le Hur
Courtney Lannert
Seunghun Lee
Leonid Levitov
Ady Mann
Gil Refael
Michael Revzen
August Romeo
Francis Song
Alessandro Silva