Built on

P. Fendley, Free fermions in disguise, J. Phys. A 52
Original
1901
Earlier work this paper cites.
P. Jordan and E. Wigner, Über das paulische äquivalenzverbot, Z. Physik 47
1928
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E. Lieb, T. Schultz, and D. Mattis, Two soluble models of an antiferromagnetic chain, Ann. Phys. 16
1961
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T. D. Schultz, D. C. Mattis, and E. H. Lieb, Two-dimensional ising model as a soluble problem of many fermions, Rev. Mod. Phys. 36
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J. Stolze, V. Viswanath, and G. Müller, Dynamics of semi-infinite quantum spin chains at t = ∞ t=\infty , Z. Physik B 89
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J.-P. Allouche and T. Johnson, Narayana’s Cows and Delayed Morphisms, in Journées d’Informatique Musicale (île de Tatihou, France, 1996)
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A. Y. Kitaev, Unpaired majorana fermions in quantum wires, Physics-Uspekhi 44
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L. G. Valiant, Quantum circuits that can be simulated classically in polynomial time, SIAM Journal on Computing 31
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B. M. Terhal and D. P. Divincenzo, Classical simulation of noninteracting-fermion quantum circuits, Phys. Rev. A 65
2002
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Y. Yanagihara and K. Minami, Exact solution of a cluster model with next-nearest-neighbor interaction, Progr. of Theor. Exp. Phys. 2020
Original
2003
Earlier work this paper cites.
M. Ogura, Y. Imamura, N. Kameyama, K. Minami, and M. Sato, Geometric criterion for solvability of lattice spin systems, Phys. Rev. B 102
Original
2003
Earlier work this paper cites.
A. Chapman and S. T. Flammia, Characterization of solvable spin models via graph invariants, Quantum 4
Original
2003
Earlier work this paper cites.
M. Möttönen, J. J. Vartiainen, V. Bergholm, and M. M. Salomaa, Quantum Circuits for General Multiqubit Gates, Phys. Rev. Lett. 93
2004
Earlier work this paper cites.

Similar

F. C. Alcaraz and R. A. Pimenta, Free fermionic and parafermionic quantum spin chains with multispin interactions, Phys. Rev. B 102
Original
2005
Cited alongside, same era.
A. Kitaev, Anyons in an exactly solved model and beyond, Ann. Phys. 321
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P. Fendley and K. Schoutens, Cooper pairs and exclusion statistics from coupled free-fermion chains, J. Stat. Mech. 2007
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R. Jozsa and A. Miyake, Matchgates and classical simulation of quantum circuits, Proc. Roy. Soc. Lond. A 464
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2008
Cited alongside, same era.
F. C. Alcaraz and R. A. Pimenta, Integrable quantum spin chains with free fermionic and parafermionic spectrum, Phys. Rev. B 102
Original
2010
Cited alongside, same era.

Then

T. Forgács and K. Tran, On the zeros of polynomials generated by rational functions with a hyperbolic polynomial type denominator, Constr. Approx. 46
Original
2017
Later among the works it cites.
G. Z. Feher, A. Garbali, J. de Gier, and K. Schoutens, A curious mapping between supersymmetric quantum chains, in 2017 MATRIX Annals (Springer International Publishing, Cham, 2019) pp. 167–184, arXiv:1710.02658 [cond-mat.stat-mech]
Original
2019
Later among the works it cites.
A. Jahn and J. Eisert, Holographic tensor network models and quantum error correction: a topical review, Quantum Sci. Tech. 6
Original
2021
Later among the works it cites.
F. C. Alcaraz and R. A. Pimenta, Free-parafermionic z ⁡ ( n ) z(n) and free-fermionic x y xy quantum chains, Phys. Rev. E 104
Original
2021
Later among the works it cites.

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2024

Exact real time dynamics with free fermions in disguise

Vona, István, Mestyán, Márton, Pozsgay, Balázs

Understand

We consider quantum spin chains with a hidden free fermionic structure, distinct from the Jordan-Wigner transformation and its generalizations.

We express selected local operators with the hidden fermions.
This way we can exactly solve the real time dynamics in various physical scenarios, including the computation of selected dynamical two point functions, in continuous or discrete time.
In the latter case we build a quantum circuit that can be implemented on a quantum computer.

Built on

P. Fendley, Free fermions in disguise, J. Phys. A 52
Original
1901
Earlier work this paper cites.
P. Jordan and E. Wigner, Über das paulische äquivalenzverbot, Z. Physik 47
1928
Earlier work this paper cites.
E. Lieb, T. Schultz, and D. Mattis, Two soluble models of an antiferromagnetic chain, Ann. Phys. 16
1961
Earlier work this paper cites.
T. D. Schultz, D. C. Mattis, and E. H. Lieb, Two-dimensional ising model as a soluble problem of many fermions, Rev. Mod. Phys. 36
1964
Earlier work this paper cites.
J. Stolze, V. Viswanath, and G. Müller, Dynamics of semi-infinite quantum spin chains at t = ∞ t=\infty , Z. Physik B 89
1992
Earlier work this paper cites.
J.-P. Allouche and T. Johnson, Narayana’s Cows and Delayed Morphisms, in Journées d’Informatique Musicale (île de Tatihou, France, 1996)
1996
Earlier work this paper cites.
A. Y. Kitaev, Unpaired majorana fermions in quantum wires, Physics-Uspekhi 44
2001
Earlier work this paper cites.
L. G. Valiant, Quantum circuits that can be simulated classically in polynomial time, SIAM Journal on Computing 31
2002
Earlier work this paper cites.
B. M. Terhal and D. P. Divincenzo, Classical simulation of noninteracting-fermion quantum circuits, Phys. Rev. A 65
2002
Earlier work this paper cites.
Y. Yanagihara and K. Minami, Exact solution of a cluster model with next-nearest-neighbor interaction, Progr. of Theor. Exp. Phys. 2020
Original
2003
Earlier work this paper cites.
M. Ogura, Y. Imamura, N. Kameyama, K. Minami, and M. Sato, Geometric criterion for solvability of lattice spin systems, Phys. Rev. B 102
Original
2003
Earlier work this paper cites.
A. Chapman and S. T. Flammia, Characterization of solvable spin models via graph invariants, Quantum 4
Original
2003
Earlier work this paper cites.
M. Möttönen, J. J. Vartiainen, V. Bergholm, and M. M. Salomaa, Quantum Circuits for General Multiqubit Gates, Phys. Rev. Lett. 93
2004
Earlier work this paper cites.

Similar

F. C. Alcaraz and R. A. Pimenta, Free fermionic and parafermionic quantum spin chains with multispin interactions, Phys. Rev. B 102
Original
2005
Cited alongside, same era.
A. Kitaev, Anyons in an exactly solved model and beyond, Ann. Phys. 321
2006
Cited alongside, same era.
P. Fendley and K. Schoutens, Cooper pairs and exclusion statistics from coupled free-fermion chains, J. Stat. Mech. 2007
2007
Cited alongside, same era.
R. Jozsa and A. Miyake, Matchgates and classical simulation of quantum circuits, Proc. Roy. Soc. Lond. A 464
Original
2008
Cited alongside, same era.
F. C. Alcaraz and R. A. Pimenta, Integrable quantum spin chains with free fermionic and parafermionic spectrum, Phys. Rev. B 102
Original
2010
Cited alongside, same era.

Then

T. Forgács and K. Tran, On the zeros of polynomials generated by rational functions with a hyperbolic polynomial type denominator, Constr. Approx. 46
Original
2017
Later among the works it cites.
G. Z. Feher, A. Garbali, J. de Gier, and K. Schoutens, A curious mapping between supersymmetric quantum chains, in 2017 MATRIX Annals (Springer International Publishing, Cham, 2019) pp. 167–184, arXiv:1710.02658 [cond-mat.stat-mech]
Original
2019
Later among the works it cites.
A. Jahn and J. Eisert, Holographic tensor network models and quantum error correction: a topical review, Quantum Sci. Tech. 6
Original
2021
Later among the works it cites.
F. C. Alcaraz and R. A. Pimenta, Free-parafermionic z ⁡ ( n ) z(n) and free-fermionic x y xy quantum chains, Phys. Rev. E 104
Original
2021
Later among the works it cites.

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

S. J. Elman, A. Chapman, and S. T. Flammia, Free fermions behind the disguise, Commun. Math. Phys. 388

Original

2012

Cited alongside, same era.

P. Fendley, Free parafermions, J. Phys. A 47

Original

2014

Cited alongside, same era.

K. Tran, Connections between discriminants and the root distribution of polynomials with rational generating function, J. Math. An. Appl. 410

Original

2014

Cited alongside, same era.

K. Minami, Solvable Hamiltonians and Fermionization Transformations Obtained from Operators Satisfying Specific Commutation Relations, J. Phys. Soc. Japan 85

2016

Cited alongside, same era.

J. de Gier, G. Z. Feher, B. Nienhuis, and M. Rusaczonek, Integrable supersymmetric chain without particle conservation, J. Stat. Mech. , 023104 (2016) , arXiv:1510.02520 [cond-mat.quant-gas]

Original

2016

Cited alongside, same era.

I. S. Eliëns, F. B. Ramos, J. C. Xavier, and R. G. Pereira, Boundary versus bulk behavior of time-dependent correlation functions in one-dimensional quantum systems, Phys. Rev. B 93

Original

2016

Cited alongside, same era.

K. Minami, Infinite number of solvable generalizations of XY-chain, with cluster state, and with central charge c = m/2, Nucl. Phys. B 925

Original