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.

Noise measurements in current can reveal many body entanglement

Quantum wakes: How is the pattern following a moving quantum detector related to the patter behind a duck in water?

A pattern of measurements can create chiral edge modes

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