Miguel Tierz

Visiting Professor

Email: tierz _at_ simis.cn
Research Fields:
General fields: Mathematical Physics, Theoretical Physics, Applied Mathematics (more recent). Specific fields: Random matrix theory, Gauge theory, Strongly-correlated systems, Mathematical problems in the development of quantum technologies
Office No.: R1403

Bio

Miguel Tierz’s research has focused on random matrix theory, gauge theories and strongly correlated quantum systems. His work provides rigorous analytical tools and exact solutions to understand phase transitions, gauge theories, and integrable models. His most recent research focuses on cavity optomechanics, periodically driven quantum systems (Floquet physics) and their applications in quantum computation. He has published in a wide variety of journals, including Phys. Rev. X, Comm. Math. Phys, Phys Rev A and D, Quantum, JHEP and JSTAT, J. Math. Phys., Nucl. Phys. B, J. Comb. Theory A , among others.

Miguel Tierz defended his PhD at Universitat de Barcelona, Spain in 2008 with a thesis on Random matrix models in Chern-Simons theory. He completed postdoctoral research at Brandeis University in the US, the Hebrew University of Jerusalem in Israel, and Universidad Complutense de Madrid (UCM) in Spain. He has also been an Associate Professor in Lisbon, Portugal, and a Senior Researcher at UCM. He is currently a Visiting Professor at SIMIS in Shanghai.

Education Experience

  • 1995-1999 Licenciado en Fisica (BSc in Physics, Theoretical) Universitat de Barcelona, Spain
  • 2003-2008 PhD in Theoretical/Mathematical Physics Universitat de Barcelona, Spain.

Work Experience

  • 2021- Senior postdoctoral researcher/ Maria Zambrano fellow Universidad Complutense de Madrid, Spain
  • 2019-2021 Associate Professor ISCTE (Instituto Universitário de Lisboa), Portugal
  • 2015-2019 Researcher FCT (5 year position, senior postdoctoral) Fundação para a Ciência e a Tecnologia / Universidade de Lisboa Portugal
  • 2012-2015 Researcher Juan de la Cierva Universidad Complutense de Madrid ,Spain
  • 2011-2012 Postdoctoral Researcher Grupo de Física Matemática, Universidade de Lisboa
  • 2010-2011 Lady Davis Fellow in Mathematics Institute of Mathematics, The Hebrew University of Jerusalem (Israel)
  • 2008-2010 Postdoctoral researcher Brandeis University (Massachusetts, USA)
  • 2000-2002 Visiting PhD student LPTMS (Université de Paris XI, France)

Honors and Awards

Publications

  1. Jorge G. Russo and Miguel Tierz, An analytical exploration of the optomechanical attractor diagram and of limit cycles, https://arxiv.org/pdf/2505.05352
  2. Miguel Tierz, Analytical control of the exchange interaction in periodically driven Mott insulators, https://arxiv.org/abs/2501.05416
  3. Leonardo Santilli, David Pérez-García and Miguel Tierz, Hawking-Page transition on a spin chain, Phys. Rev. Research 6, 033007 (2024)  https://doi.org/10.1103/PhysRevResearch.6.033007
  4. Jorge Ruso, Miguel Tierz. 2024. Landau-Zener transition rates of superconducting qubits and absorption spectrum in quantum dots,. Phys. Rev. A 109, 033702 (2024). https://doi.org/10.1103/PhysRevA.109.033702
  5. David Perez-Garcia; Leonardo Santilli; Miguel Tierz. 2024. Dynamical quantum phase transitions from random matrix theory. Quantum 8, 1271 (2024). https://doi.org/10.22331/q-2024-02-29-1271
  6. Leonardo Santilli and Miguel Tierz. 2022. Crystal bases and three-dimensional N= 4 Coulomb branches. J. High. Energ. Phys. (2022), 1-6. https://doi.org/10.48550/arXiv.2111.05206
  7. Leonardo Santilli; Miguel Tierz. 2021. Schur expansion of random-matrix reproducing kernels. J. Phys. A: Math. Theor. 54 435202 (2021). IOP. 54, pp.435202. https://doi.org/10.1088/1751-8121/ac2754
  8. Leonardo Santilli; Miguel Tierz. Multiple phases and meromorphic deformations of unitary matrix models. Nucl. Phys. B 976, 115694 (2022). https://doi.org/10.1016/j.nuclphysb.2022.115694
  9. Leonardo Santilli, Miguel Tierz. 2020. Riemannian Gaussian distributions, random matrix ensembles and diffusion kernels. Nuclear Physics B Volume 973, December 2021, 115582. https://doi.org/10.1016/j.nuclphysb.2021.115582
  10. Leonardo Santilli; Richard Szabo; Miguel Tierz. 2020. TT-deformation of q-Yang-Mills theory. J. High Energ. Phys. 2020, 86 (2020). Springer-Verlag. https://doi.org/10.48550/arXiv.2009.00657
  11. Leonardo Santilli and Miguel Tierz. 2020. Exact results and Schur expansions in quiver Chern-Simons-matter theories. J. High Energ. Phys. 2020, 22 (2020). https://doi.org/10.1007/JHEP10(2020)022
  12. Leonardo Santilli, Miguel Tierz. 2020. Complex (super)-matrix models with external sources and q-ensembles of Chern–Simons and ABJ (M) type. Journal of Physics A: Mathematical and Theoretical. 54-42, pp.425201. https://doi.org/10.1088/1751-8121/abb6b0
  13. Jorge Russo and Miguel Tierz. 2020. Multiple phases in a generalized Gross-Witten-Wadia matrix model. J. High Energ. Phys. 2020, 81 (2020). Springer-Verlag. 81. https://doi.org/10.1007/JHEP09(2020)081
  14. Leonardo Santilli and Miguel Tierz. 2020. Exact equivalences and phase discrepancies between random matrix ensembles. J. Stat. Mech. (2020) 083107. 2020, pp.083107. https://doi.org/10.1088/1742-5468/aba594
  15. David Garcia Garcia; Miguel Tierz. 2020. Matrix models for classical groups and Toeplitz±Hankel minors with applications to Chern-Simons theory and fermionic models. J. Phys. A: Math. Theor. 53 345201 (2020). https://doi.org/10.1088/1751-8121/ab9b4d
  16. Leonardo Santilli, Miguel Tierz; Richard Szabo. 2020. Five-dimensional cohomological localization and squashed -deformations of two-dimensional Yang-Mills theory. J. High Energ. Phys. 2020, 36 (2020). https://doi.org/10.1007/JHEP06(2020)036
  17. David Garcia Garcia; Miguel Tierz;. 2020. Toeplitz minors and specializations of skew Schur polynomials. Journal of Combinatorial Theory, Series A Volume 172, May 2020, 105201. 172, pp.105201. https://doi.org/10.1016/j.jcta.2019.105201
  18. Leonardo Santilli; Miguel Tierz. 2019. On SQED3 and SQCD3: phase transitions and integrability. Phys. Rev. D 100, 061702(R) (2019). APS. https://doi.org/10.1103/PhysRevD.100.061702
  19. Leonardo Santilli; Miguel Tierz. 2019. Phase transitions and Wilson loops in antisymmetric representations in Chern-Simons-matter theory. J. Phys. A: Math. Theor. 52 385401 (2019). 52-38, pp.385401. https://doi.org/10.1088/1751-8121/ab335c
  20. Leonardo Santilli; Miguel Tierz. 2019. Phase transition in complex-time Loschmidt echo of short and long range spin chain. J. Stat. Mech. (2020) 063102. IOP. https://doi.org/10.1088/1742-5468/ab837b
  21. Leonardo Santilli; Miguel Tierz. 2018. Large N phase transition in TT-deformed 2d Yang-Mills theory on the sphere. J. High Energ. Phys. (2019) 2019: 54. Springer-Verlag. https://doi.org/10.1007/JHEP01(2019)054
  22. Miguel Tierz. 2018. Wilson loops and free energies in 3d N=4 SYM: exact results, exponential asymptotics and duality. Progress of Theoretical and Experimental Physics, Vol 2019, (2019), 053B01. Oxford University Press. https://doi.org/10.1093/ptep/ptz036
  23. Miguel Tierz. 2017. Polynomial solutions of quantum Grassmann matrices. J. Stat. Mech. May 2017, pp.053203. https://doi.org/10.1088/1742-5468/AA6C84
  24. Jorge Russo; Miguel Tierz. 2017. Quantum phase transition in many-flavor supersymmetric QED. Physical Review D, Rapid Communication. APS. 95, pp.031901. https://doi.org/10.1103/PHYSREVD.95.031901
  25. Miguel Tierz. 2016. Mass-deformed ABJ and ABJM theory, Meixner-Pollaczek polynomials, and su(1,1) oscillators. Physical Review D. APS. 93, pp.126003. https://doi.org/10.1103/PHYSREVD.93.126003
  26. Miguel Tierz. 2016. Exact solution of Chern-Simons-matter matrix models with characteristic/orthogonal polynomials. Journal of High Energy Physics. Springer-Verlag. 04, pp.168. https://doi.org/10.1007/JHEP04(2016)168
  27. David Perez-Garcia; Miguel Tierz. 2016. Chern-Simons theory encoded on a spin chain. Journal of Statistical Mechanics. IOPScience. 2016-013103. (3) https://doi.org/10.1088/1742-5468/2016/01/013103
  28. Georgios Giasemidis; Miguel Tierz. 2016. Mordell integrals and Giveon-Kutasov duality. Journal of High Energy Physics 01, pp.068. https://doi.org/10.1007/JHEP01(2016)068
  29. Miguel Tierz; Guillermo Silva; Jorge Russo. 2015. Supersymmetric U(N) Chern-Simons-matter theory and phase transitions. Communications in Mathematical Physics. Springer-Verlag. 338, pp.1411-1442. https://doi.org/10.1007/S00220-015-2399-4
  30. Georgios Giasemidis; Miguel Tierz. 2014. Torus knot polynomials and susy Wilson loops. Letters in Mathematical Physics. Springer-Verlag. 104, pp.1535-1556. https://doi.org/10.1007/S11005-014-0724-Z
  31. David Pérez-García; Miguel Tierz. 2014. Mapping between the Heisenberg XX Spin Chain and Low-Energy QCD. Physical Review X. APS. 4, pp.021050. https://doi.org/10.1103/PHYSREVX.4.021050
  32. Georgios Giasemidis; Richard J. Szabo; Miguel Tierz. 2014. Supersymmetric gauge theories, Coulomb gases and Chern-Simons matrix models. Physical Review D. APS. 89-2, pp.025016. https://doi.org/10.1103/PHYSREVD.89.025016
  33. Richard J. Szabo; Miguel Tierz. 2013. q-deformations of two-dimensional Yang-Mills theory: Classification, categorification and refinement. Nuclear Physics B. Elsevier. 876-1, pp.234-308. https://doi.org/10.1016/J.NUCLPHYSB.2013.08.001
  34. Richard J. Szabo; Miguel Tierz. 2012. Matrix models and stochastic growth in Donaldson-Thomas theory. Journal of Mathematical Physics. AIP. 53, pp.103502. https://doi.org/10.1063/1.4748525
  35. Mauricio Romo; Miguel Tierz. 2012. Unitary Chern-Simons matrix model and the Villain lattice action. Physical Review D. APS. 86-4, pp.045027. https://doi.org/10.1103/PHYSREVD.86.045027
  36. Richard J. Szabo; Miguel Tierz. 2012. Two-dimensional Yang-Mills theory, Painleve equations and the six-vertex model. Journal of Physics A: Mathematical and Theoretical. IOP Publishing. 45, pp.085401. https://doi.org/10.1088/1751-8113/45/8/085401
  37. Miguel Tierz. 2010. Schur polynomials and biorthogonal random matrix ensembles. Journal of Mathematical Physics. AIP Publishing. 51, pp.063509. https://doi.org/10.1063/1.3377965
  38. Richard J. Szabo; Miguel Tierz. 2010. Chern-Simons matrix models, two-dimensional Yang-Mills theory and the Sutherland model. Journal of Physics A: Mathematical and Theoretical. IOP Publishing. 43-265401, pp.265401. https://doi.org/10.1088/1751-8113/43/26/265401
  39. M. Tierz. 2009. Chern-Simons theory, exactly solvable models and free fermions at finite temperature. Modern Physics Letters A. World Scientific. 24, pp.3157-3171. https://doi.org/10.1142/S0217732309032071
  40. Miguel Tierz. 2007. SL(2,R) matrix model and supersymmetric Yang-Mills integrals. Physical Review D. APS. 76-10, pp.107701. https://doi.org/10.1103/PHYSREVD.76.107701
  41. Y. Dolivet; M. Tierz. 2007. Chern-Simons matrix models and Stieltjes-Wigert polynomials. Journal of Mathematical Physics. AIP Publishing. 48-2, pp.023507. https://doi.org/10.1063/1.2436734
  42. S. de Haro; M. Tierz. 2005. Discrete and oscillatory matrix models in Chern-Simons theory. Nuclear Physics B. Elsevier. 731-3, pp.225-241. https://doi.org/10.1016/J.NUCLPHYSB.2005.09.034
  43. S. de Haro; M. Tierz. 2004. Brownian motion, Chern-Simons theory, and 2-D Yang-Mills. Physics Letters B. Elsevier. 601-3-4, pp.201-208. https://doi.org/10.1016/J.PHYSLETB.2004.09.033
  44. E. Elizalde; M. Tierz. 2004. Multiplicative anomaly and zeta factorization. Journal of Mathematical Physics. AIP Publishing. 45, pp.1168. https://doi.org/10.1063/1.1646447
  45. M. Tierz. 2004. Soft matrix models and Chern-Simons partition functions. Modern Physics Letters A. World Scientific. 19, pp.1365-1378. https://doi.org/10.1142/S0217732304014100
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