Built on

W. Landry and D. Simmons-Duffin, Scaling the semidefinite program solver SDPB , 1909.09745
Original
1909
Earlier work this paper cites.
S. M. Chester, W. Landry, J. Liu, D. Poland, D. Simmons-Duffin, N. Su et al., Carving out OPE space and precise O ⁡ ( 2 ) O(2) model critical exponents , JHEP 06
Original
1912
Earlier work this paper cites.
S. Katsura, Statistical mechanics of the anisotropic linear heisenberg model , Phys. Rev. 127
1962
Earlier work this paper cites.
G. Fantuzzi, D. Goluskin, D. Huang and S. I. Chernyshenko, Bounds for deterministic and stochastic dynamical systems using sum-of-squares optimization , SIAM Journal on Applied Dynamical Systems 15
1988
Earlier work this paper cites.
B. Reznick, Uniform denominators in hilbert’s seventeenth problem , Mathematische Zeitschrift 220
1995
Earlier work this paper cites.
H. W. Lin, Bootstraps to strings: solving random matrix models with positivity , JHEP 06
Original
2002
Earlier work this paper cites.
X. Han, S. A. Hartnoll and J. Kruthoff, Bootstrapping Matrix Quantum Mechanics , Phys. Rev. Lett. 125
Original
2004
Earlier work this paper cites.
R. Rattazzi, V. S. Rychkov, E. Tonni and A. Vichi, Bounding scalar operator dimensions in 4D CFT , JHEP 12
Original
2008
Earlier work this paper cites.
Cambridge University Press, 2 ed., 2011, 10.1017/CBO9780511973765
S. Sachdev, Quantum Phase Transitions · 2011
Earlier work this paper cites.

Similar

S. El-Showk, M. F. Paulos, D. Poland, S. Rychkov, D. Simmons-Duffin and A. Vichi, Solving the 3D Ising Model with the Conformal Bootstrap , Phys. Rev. D 86
Original
2012
Cited alongside, same era.
S. El-Showk and M. F. Paulos, Bootstrapping Conformal Field Theories with the Extremal Functional Method , Phys. Rev. Lett. 111
Original
2013
Cited alongside, same era.
D. Simmons-Duffin, A Semidefinite Program Solver for the Conformal Bootstrap , JHEP 06
Original
2015
Cited alongside, same era.
P. D. Anderson and M. Kruczenski, Loop Equations and bootstrap methods in the lattice , Nucl. Phys. B 921
Original
2017
Cited alongside, same era.
D. Simmons-Duffin, The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT , JHEP 03

Then

J. Bhattacharya, D. Das, S. K. Das, A. K. Jha and M. Kundu, Numerical bootstrap in quantum mechanics , Phys. Lett. B 823
Original
2021
Later among the works it cites.
M. Reehorst, S. Rychkov, D. Simmons-Duffin, B. Sirois, N. Su and B. van Rees, Navigator Function for the Conformal Bootstrap , SciPost Phys. 11
Original
2021
Later among the works it cites.
V. Kazakov and Z. Zheng, Analytic and numerical bootstrap for one-matrix model and “unsolvable” two-matrix model , JHEP 06
Original
2022
Closest in time.
D. Berenstein and G. Hulsey, Bootstrapping more QM systems , J. Phys. A 55
Original
2022
Closest in time.
D. Berenstein and G. Hulsey, Anomalous bootstrap on the half-line , Phys. Rev. D 106

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…

2022

Bootstrapping the gap in quantum spin systems

Nancarrow, Colin Oscar, Xin, Yuan

Understand

In this work we report on a new bootstrap method for quantum mechanical problems that closely mirrors the setup from conformal field theory (CFT).

We use the equations of motion to develop an analogue of the conformal block expansion for matrix elements and impose crossing symmetry in order to place bounds on their values.
The method can be applied to any quantum mechanical system with a local Hamiltonian, and we test it on an anharmonic oscillator model as well as the (1+1)-dimensional transverse field Ising model (TFIM).
For the anharmonic oscillator model we show that a small number of crossing equations provides an accurate solution to the spectrum and matrix elements.

Built on

W. Landry and D. Simmons-Duffin, Scaling the semidefinite program solver SDPB , 1909.09745
Original
1909
Earlier work this paper cites.
S. M. Chester, W. Landry, J. Liu, D. Poland, D. Simmons-Duffin, N. Su et al., Carving out OPE space and precise O ⁡ ( 2 ) O(2) model critical exponents , JHEP 06
Original
1912
Earlier work this paper cites.
S. Katsura, Statistical mechanics of the anisotropic linear heisenberg model , Phys. Rev. 127
1962
Earlier work this paper cites.
G. Fantuzzi, D. Goluskin, D. Huang and S. I. Chernyshenko, Bounds for deterministic and stochastic dynamical systems using sum-of-squares optimization , SIAM Journal on Applied Dynamical Systems 15
1988
Earlier work this paper cites.
B. Reznick, Uniform denominators in hilbert’s seventeenth problem , Mathematische Zeitschrift 220
1995
Earlier work this paper cites.
H. W. Lin, Bootstraps to strings: solving random matrix models with positivity , JHEP 06
Original
2002
Earlier work this paper cites.
X. Han, S. A. Hartnoll and J. Kruthoff, Bootstrapping Matrix Quantum Mechanics , Phys. Rev. Lett. 125
Original
2004
Earlier work this paper cites.
R. Rattazzi, V. S. Rychkov, E. Tonni and A. Vichi, Bounding scalar operator dimensions in 4D CFT , JHEP 12
Original
2008
Earlier work this paper cites.
Cambridge University Press, 2 ed., 2011, 10.1017/CBO9780511973765
S. Sachdev, Quantum Phase Transitions · 2011
Earlier work this paper cites.

Similar

S. El-Showk, M. F. Paulos, D. Poland, S. Rychkov, D. Simmons-Duffin and A. Vichi, Solving the 3D Ising Model with the Conformal Bootstrap , Phys. Rev. D 86
Original
2012
Cited alongside, same era.
S. El-Showk and M. F. Paulos, Bootstrapping Conformal Field Theories with the Extremal Functional Method , Phys. Rev. Lett. 111
Original
2013
Cited alongside, same era.
D. Simmons-Duffin, A Semidefinite Program Solver for the Conformal Bootstrap , JHEP 06
Original
2015
Cited alongside, same era.
P. D. Anderson and M. Kruczenski, Loop Equations and bootstrap methods in the lattice , Nucl. Phys. B 921
Original
2017
Cited alongside, same era.
D. Simmons-Duffin, The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT , JHEP 03

Then

J. Bhattacharya, D. Das, S. K. Das, A. K. Jha and M. Kundu, Numerical bootstrap in quantum mechanics , Phys. Lett. B 823
Original
2021
Later among the works it cites.
M. Reehorst, S. Rychkov, D. Simmons-Duffin, B. Sirois, N. Su and B. van Rees, Navigator Function for the Conformal Bootstrap , SciPost Phys. 11
Original
2021
Later among the works it cites.
V. Kazakov and Z. Zheng, Analytic and numerical bootstrap for one-matrix model and “unsolvable” two-matrix model , JHEP 06
Original
2022
Closest in time.
D. Berenstein and G. Hulsey, Bootstrapping more QM systems , J. Phys. A 55
Original
2022
Closest in time.
D. Berenstein and G. Hulsey, Anomalous bootstrap on the half-line , Phys. Rev. D 106

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

Original

2017

Cited alongside, same era.

P. Anderson and M. Kruczenski, Loop equation in lattice gauge theories and bootstrap methods , in EPJ Web of Conferences , vol. 175, p. 11011, EDP Sciences, 2018

2018

Cited alongside, same era.

E. Dyer, A. L. Fitzpatrick and Y. Xin, Constraints on Flavored 2d CFT Partition Functions , JHEP 02

Original

2018

Cited alongside, same era.

D. Poland, S. Rychkov and A. Vichi, The Conformal Bootstrap: Theory, Numerical Techniques, and Applications , Rev. Mod. Phys. 91

Original

2019

Cited alongside, same era.

X. Han, Quantum many-body bootstrap , arXiv preprint arXiv:2006.06002 (2020)

Original