Fetching the paper…

Reading the bibliography…

2022

Spread Complexity and Topological Transitions in the Kitaev Chain

Caputa, Pawel, Gupta, Nitin, Haque, S. Shajidul et al.

Original
PDF
Post on X

Understand

A number of recent works have argued that quantum complexity, a well-known concept in computer science that has re-emerged recently in the context of the physics of black holes, may be used as an efficient probe of novel phenomena such as quantum chaos and even quantum phase transitions.

In this article, we provide further support for the latter, using a 1-dimensional p-wave superconductor - the Kitaev chain - as a prototype of a system displaying a topological phase transition.
The Hamiltonian of the Kitaev chain manifests two gapped phases of matter with fermion parity symmetry; a trivial strongly-coupled phase and a topologically non-trivial, weakly-coupled phase with Majorana zero-modes.
We show that Krylov-complexity (or, more precisely, the associated spread-complexity) is able to distinguish between the two and provides a diagnostic of the quantum critical point that separates them.

Spread Complexity and Topological Transitions in the Kitaev Chain · Around

Built on

F. Liu, S. Whitsitt, J. B. Curtis, R. Lundgren, P. Titum, Z.-C. Yang, J. R. Garrison, and A. V. Gorshkov, Circuit complexity across a topological phase transition
Original
1902
Earlier work this paper cites.
T. Ali, A. Bhattacharyya, S. S. Haque, E. H. Kim, N. Moynihan, and J. Murugan, Chaos and Complexity in Quantum Mechanics
Original
1905
Earlier work this paper cites.
Z. Xiong, D.-X. Yao, and Z. Yan, Nonanalyticity of circuit complexity across topological phase transitions
Original
1906
Earlier work this paper cites.
J. L. F. Barbón, E. Rabinovici, R. Shir, and R. Sinha, On The Evolution Of Operator Complexity Beyond Scrambling
Original
1907
Earlier work this paper cites.
A. Bhattacharyya, W. Chemissany, S. Shajidul Haque, and B. Yan, Towards the web of quantum chaos diagnostics
Original
1909
Earlier work this paper cites.
A. Bouland, B. Fefferman, and U. Vazirani, Computational pseudorandomness, the wormhole growth paradox, and constraints on the AdS/CFT duality
Original
1910
Earlier work this paper cites.
A. Dymarsky and A. Gorsky, Quantum chaos as delocalization in Krylov space
Original
1912
Earlier work this paper cites.
C. Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
1950
Earlier work this paper cites.
A. I. Larkin and Y. N. Ovchinnikov, Quasiclassical method in the theory of superconductivity
1969
Earlier work this paper cites.
A. M. Perelomov, Coherent states for arbitrary Lie group
1972
Earlier work this paper cites.
J. M. Kosterlitz and D. J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems
1973
Earlier work this paper cites.
W. P. Su, J. R. Schrieffer, and A. J. Heeger, Solitons in polyacetylene
1979
Earlier work this paper cites.
J. M. Maldacena, The Large N limit of superconformal field theories and supergravity
1998
Earlier work this paper cites.
Cambridge University Press, 2000
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information · 2000
Earlier work this paper cites.
A. Y. Kitaev, Unpaired majorana fermions in quantum wires
2001
Earlier work this paper cites.
A. Bhattacharyya, S. Das, S. Shajidul Haque, and B. Underwood, Cosmological Complexity
Original
2001
Earlier work this paper cites.
J. M. Magán and J. Simón, On operator growth and emergent Poincaré symmetries
Original
2002
Earlier work this paper cites.
T. Senthil, A. Vishwanath, L. Balents, S. Sachdev, and M. P. A. Fisher, Deconfined quantum critical points
2004
Earlier work this paper cites.
M. A. Nielsen, A geometric approach to quantum circuit lower bounds
2005
Earlier work this paper cites.
A. Bhattacharyya, S. Das, S. S. Haque, and B. Underwood, Rise of cosmological complexity: Saturation of growth and chaos
Original
2005
Earlier work this paper cites.

Similar

M. A. Nielsen, M. R. Dowling, M. Gu, and A. C. Doherty, Quantum computation as geometry
2006
Cited alongside, same era.
M. R. Dowling and M. A. Nielsen, The geometry of quantum computation
2007
Cited alongside, same era.
A. Bhattacharyya, W. Chemissany, S. S. Haque, J. Murugan, and B. Yan, The Multi-faceted Inverted Harmonic Oscillator: Chaos and Complexity
Original
2007
Cited alongside, same era.
M. Carrega, J. Kim, and D. Rosa, Unveiling Operator Growth Using Spin Correlation Functions
Original
2007
Cited alongside, same era.
J. Watrous, Quantum computational complexity
Original
2008
Cited alongside, same era.

Then

K. Kawabata, R. Kobayashi, N. Wu, and H. Katsura, Exact zero modes in twisted Kitaev chains
Original
2017
Later among the works it cites.
J. Liu, Spectral form factors and late time quantum chaos
Original
2018
Later among the works it cites.
M. Heyl, Dynamical quantum phase transitions: a review
Original
2018
Later among the works it cites.
D. E. Parker, X. Cao, A. Avdoshkin, T. Scaffidi, and E. Altman, A Universal Operator Growth Hypothesis
Original
2019
Later among the works it cites.
T. Ali, A. Bhattacharyya, S. Shajidul Haque, E. H. Kim, and N. Moynihan, Post-Quench Evolution of Complexity and Entanglement in a Topological System
Original

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Springer Science & Business Media, 2008

V. Viswanath and G. Müller, The recursion method: application to many-body dynamics · 2008

Cited alongside, same era.

S.-K. Jian, B. Swingle, and Z.-Y. Xian, Complexity growth of operators in the SYK model and in JT gravity

2008

Cited alongside, same era.

E. Rabinovici, A. Sánchez-Garrido, R. Shir, and J. Sonner, Operator complexity: a journey to the edge of Krylov space

2009

Cited alongside, same era.

C. Yin and A. Lucas, Quantum operator growth bounds for kicked tops and semiclassical spin chains

2010

Cited alongside, same era.

A. Bhattacharyya, S. S. Haque, and E. H. Kim, Complexity from the reduced density matrix: a new diagnostic for chaos

2011

Cited alongside, same era.

M. Leijnse and K. Flensberg, Introduction to topological superconductivity and Majorana fermions

2012

Cited alongside, same era.

D. Harlow and P. Hayden, Quantum Computation vs. Firewalls

2013

Cited alongside, same era.

2020

Later among the works it cites.

A. Dymarsky and M. Smolkin, Krylov complexity in conformal field theory

2021

Later among the works it cites.

P. Caputa and S. Datta, Operator growth in 2d CFT

2021

Later among the works it cites.

S. Bandyopadhyay, S. Bhattacharjee, and D. Sen, Driven quantum many-body systems and out-of-equilibrium topology

2021

Later among the works it cites.

S. Chapman and G. Policastro, Quantum computational complexity from quantum information to black holes and back

2022

Closest in time.

B. Chen, B. Czech, and Z.-z. Wang, Quantum information in holographic duality

2022

Closest in time.

J. Kim, J. Murugan, J. Olle, and D. Rosa, Operator delocalization in quantum networks

2022

Closest in time.

A. Kar, L. Lamprou, M. Rozali, and J. Sully, Random matrix theory for complexity growth and black hole interiors

2022

Closest in time.

E. Rabinovici, A. Sánchez-Garrido, R. Shir, and J. Sonner, Krylov complexity from integrability to chaos

2022

Closest in time.

E. Rabinovici, A. Sánchez-Garrido, R. Shir, and J. Sonner, Krylov localization and suppression of complexity

2022

Closest in time.

B. Bhattacharjee, X. Cao, P. Nandy, and T. Pathak, Krylov complexity in saddle-dominated scrambling

2022

Closest in time.

Z.-Y. Fan, Universal relation for operator complexity

2022

Closest in time.

D. Patramanis, Probing the entanglement of operator growth

Original

2022

Closest in time.

P. Caputa, J. M. Magan, and D. Patramanis, Geometry of Krylov complexity

2022

Closest in time.

S. S. Haque, C. Jana, and B. Underwood, Saturation of thermal complexity of purification

2022

Closest in time.