Nachtergaele, Bruno; Sims, Robert; Young, Amanda Stability of the bulk gap for frustration-free topologically ordered quantum lattice systems. (English) Zbl 07801976 Lett. Math. Phys. 114, No. 1, Paper No. 24, 55 p. (2024). MSC: 81Q15 82B10 82B20 46L60 PDFBibTeX XMLCite \textit{B. Nachtergaele} et al., Lett. Math. Phys. 114, No. 1, Paper No. 24, 55 p. (2024; Zbl 07801976) Full Text: DOI arXiv OA License
Bachmann, Sven; Nachtergaele, Bruno; Vadnerkar, Siddharth Dynamical abelian anyons with bound states and scattering states. (English) Zbl 1520.81179 J. Math. Phys. 64, No. 7, Article ID 071903, 19 p. (2023). MSC: 81V27 81T13 PDFBibTeX XMLCite \textit{S. Bachmann} et al., J. Math. Phys. 64, No. 7, Article ID 071903, 19 p. (2023; Zbl 1520.81179) Full Text: DOI arXiv
Gebert, Martin; Moon, Alvin; Nachtergaele, Bruno A Lieb-Robinson bound for quantum spin chains with strong on-site impurities. (English) Zbl 1487.82004 Rev. Math. Phys. 34, No. 4, Article ID 2250007, 20 p. (2022). MSC: 82B10 PDFBibTeX XMLCite \textit{M. Gebert} et al., Rev. Math. Phys. 34, No. 4, Article ID 2250007, 20 p. (2022; Zbl 1487.82004) Full Text: DOI arXiv
Nachtergaele, Bruno; Sims, Robert; Young, Amanda Quasi-locality bounds for quantum lattice systems. II: perturbations of frustration-free spin models with gapped ground states. (English) Zbl 07496344 Ann. Henri Poincaré 23, No. 2, 393-511 (2022). MSC: 82B20 82B10 82D25 81Q10 PDFBibTeX XMLCite \textit{B. Nachtergaele} et al., Ann. Henri Poincaré 23, No. 2, 393--511 (2022; Zbl 07496344) Full Text: DOI arXiv
Nachtergaele, Bruno; Warzel, Simone; Young, Amanda Spectral gaps and incompressibility in a \(\nu = 1/3\) fractional quantum Hall system. (English) Zbl 1467.82022 Commun. Math. Phys. 383, No. 2, 1093-1149 (2021). MSC: 82B20 81V70 35R09 35R11 65F15 PDFBibTeX XMLCite \textit{B. Nachtergaele} et al., Commun. Math. Phys. 383, No. 2, 1093--1149 (2021; Zbl 1467.82022) Full Text: DOI arXiv
Nachtergaele, Bruno; Reschke, Jake Slow propagation in some disordered quantum spin chains. (English) Zbl 1462.82028 J. Stat. Phys. 182, No. 1, Paper No. 12, 28 p. (2021). MSC: 82C20 82C44 81V70 PDFBibTeX XMLCite \textit{B. Nachtergaele} and \textit{J. Reschke}, J. Stat. Phys. 182, No. 1, Paper No. 12, 28 p. (2021; Zbl 1462.82028) Full Text: DOI arXiv
Gebert, Martin; Nachtergaele, Bruno; Reschke, Jake; Sims, Robert Lieb-Robinson bounds and strongly continuous dynamics for a class of many-body fermion systems in \(\mathbb{R}^d\). (English) Zbl 1468.35161 Ann. Henri Poincaré 21, No. 11, 3609-3637 (2020). Reviewer: Markus Holzmann (Graz) MSC: 35Q40 81Q35 81Q05 81Q10 81V70 81V74 PDFBibTeX XMLCite \textit{M. Gebert} et al., Ann. Henri Poincaré 21, No. 11, 3609--3637 (2020; Zbl 1468.35161) Full Text: DOI arXiv
Abdul-Rahman, Houssam; Lemm, Marius; Lucia, Angelo; Nachtergaele, Bruno; Young, Amanda A class of two-dimensional AKLT models with a gap. (English) Zbl 1446.82002 Abdul-Rahman, Houssam (ed.) et al., Analytic trends in mathematical physics. Arizona school of analysis and mathematical physics, University of Arizona, Tucson, AZ, USA, March 5–9, 2018. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 741, 1-21 (2020). MSC: 82B10 82B20 PDFBibTeX XMLCite \textit{H. Abdul-Rahman} et al., Contemp. Math. 741, 1--21 (2020; Zbl 1446.82002) Full Text: DOI arXiv
Cha, Matthew; Naaijkens, Pieter; Nachtergaele, Bruno On the stability of charges in infinite quantum spin systems. (English) Zbl 1431.81086 Commun. Math. Phys. 373, No. 1, 219-264 (2020). MSC: 81T05 81R15 46L05 81R25 81V27 PDFBibTeX XMLCite \textit{M. Cha} et al., Commun. Math. Phys. 373, No. 1, 219--264 (2020; Zbl 1431.81086) Full Text: DOI arXiv Link
Lemm, Marius; Nachtergaele, Bruno Gapped PVBS models for all species numbers and dimensions. (English) Zbl 1434.82012 Rev. Math. Phys. 31, No. 9, Article ID 1950028, 18 p. (2019). MSC: 82B10 82B20 82D40 PDFBibTeX XMLCite \textit{M. Lemm} and \textit{B. Nachtergaele}, Rev. Math. Phys. 31, No. 9, Article ID 1950028, 18 p. (2019; Zbl 1434.82012) Full Text: DOI arXiv
Nachtergaele, Bruno; Sims, Robert; Young, Amanda Quasi-locality bounds for quantum lattice systems. I: Lieb-Robinson bounds, quasi-local maps, and spectral flow automorphisms. (English) Zbl 1418.82010 J. Math. Phys. 60, No. 6, 061101, 84 p. (2019). MSC: 82D25 81T10 PDFBibTeX XMLCite \textit{B. Nachtergaele} et al., J. Math. Phys. 60, No. 6, 061101, 84 p. (2019; Zbl 1418.82010) Full Text: DOI arXiv
Nachtergaele, Bruno; Sims, Robert; Young, Amanda Lieb-Robinson bounds, the spectral flow, and stability of the spectral gap for lattice fermion systems. (English) Zbl 1434.82013 Bonetto, Federico (ed.) et al., Mathematical problems in quantum physics. QMATH13: Conference on mathematical results in quantum physics, Georgia Institute of Technology, Atlanta, GA, USA, October 8–11, 2016. Proceedings. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 717, 93-115 (2018). Reviewer: Angelo Lucia (Pasadena) MSC: 82B10 82C10 82C20 PDFBibTeX XMLCite \textit{B. Nachtergaele} et al., Contemp. Math. 717, 93--115 (2018; Zbl 1434.82013) Full Text: DOI arXiv
Moon, Alvin; Nachtergaele, Bruno Stability of gapped ground state phases of spins and fermions in one dimension. (English) Zbl 1406.82007 J. Math. Phys. 59, No. 9, 091415, 25 p. (2018). Reviewer: Nasir N. Ganikhodjaev (Kuantan) MSC: 82B20 58J30 PDFBibTeX XMLCite \textit{A. Moon} and \textit{B. Nachtergaele}, J. Math. Phys. 59, No. 9, 091415, 25 p. (2018; Zbl 1406.82007) Full Text: DOI arXiv Link
Cha, Matthew; Naaijkens, Pieter; Nachtergaele, Bruno The complete set of infinite volume ground states for Kitaev’s abelian quantum double models. (English) Zbl 1394.81158 Commun. Math. Phys. 357, No. 1, 125-157 (2018). Reviewer: José M. Isidro (Valencia) MSC: 81T45 81V25 PDFBibTeX XMLCite \textit{M. Cha} et al., Commun. Math. Phys. 357, No. 1, 125--157 (2018; Zbl 1394.81158) Full Text: DOI arXiv Link
Nachtergaele, Bruno; Ueltschi, Daniel A direct proof of dimerization in a family of \(\mathrm{SU}(n)\)-invariant quantum spin chains. (English) Zbl 1376.82008 Lett. Math. Phys. 107, No. 9, 1629-1647 (2017). MSC: 82B10 82B20 82B26 82D40 PDFBibTeX XMLCite \textit{B. Nachtergaele} and \textit{D. Ueltschi}, Lett. Math. Phys. 107, No. 9, 1629--1647 (2017; Zbl 1376.82008) Full Text: DOI arXiv
Bishop, Michael; Nachtergaele, Bruno; Young, Amanda Spectral gap and edge excitations of \(d\)-dimensional PVBS models on half-spaces. (English) Zbl 1343.82012 J. Stat. Phys. 162, No. 6, 1485-1521 (2016). Reviewer: Golibjon Isroilovich Botirov (Bukhara) MSC: 82B20 PDFBibTeX XMLCite \textit{M. Bishop} et al., J. Stat. Phys. 162, No. 6, 1485--1521 (2016; Zbl 1343.82012) Full Text: DOI arXiv
Abdul-Rahman, Houssam; Nachtergaele, Bruno; Sims, Robert; Stolz, Günter Entanglement dynamics of disordered quantum XY chains. (English) Zbl 1338.82029 Lett. Math. Phys. 106, No. 5, 649-674 (2016). MSC: 82B44 PDFBibTeX XMLCite \textit{H. Abdul-Rahman} et al., Lett. Math. Phys. 106, No. 5, 649--674 (2016; Zbl 1338.82029) Full Text: DOI arXiv
Bachmann, Sven; Hamza, Eman; Nachtergaele, Bruno; Young, Amanda Product vacua and boundary state models in \(d\)-dimensions. (English) Zbl 1360.82017 J. Stat. Phys. 160, No. 3, 636-658 (2015). MSC: 82B20 82B27 82B10 PDFBibTeX XMLCite \textit{S. Bachmann} et al., J. Stat. Phys. 160, No. 3, 636--658 (2015; Zbl 1360.82017) Full Text: DOI arXiv
Bachmann, Sven; Nachtergaele, Bruno On gapped phases with a continuous symmetry and boundary operators. (English) Zbl 1291.82017 J. Stat. Phys. 154, No. 1-2, 91-112 (2014). MSC: 82B20 82B28 PDFBibTeX XMLCite \textit{S. Bachmann} and \textit{B. Nachtergaele}, J. Stat. Phys. 154, No. 1--2, 91--112 (2014; Zbl 1291.82017) Full Text: DOI arXiv
Nachtergaele, Bruno; Vershynina, Anna; Zagrebnov, Valentin A. Non-equilibrium states of a photon cavity pumped by an atomic beam. (English) Zbl 1298.81510 Ann. Henri Poincaré 15, No. 2, 213-262 (2014). Reviewer: Gernot Schaller (Berlin) MSC: 81V80 82C23 82C10 94A17 PDFBibTeX XMLCite \textit{B. Nachtergaele} et al., Ann. Henri Poincaré 15, No. 2, 213--262 (2014; Zbl 1298.81510) Full Text: DOI arXiv
Nachtergaele, Bruno; Sims, Robert; Stolz, Günter An area law for the bipartite entanglement of disordered oscillator systems. (English) Zbl 1281.81029 J. Math. Phys. 54, No. 4, 042110, 24 p. (2013). MSC: 81P68 81P40 82B30 PDFBibTeX XMLCite \textit{B. Nachtergaele} et al., J. Math. Phys. 54, No. 4, 042110, 24 p. (2013; Zbl 1281.81029) Full Text: DOI arXiv
Nachtergaele, Bruno; Sims, Robert; Stolz, Günter Quantum harmonic oscillator systems with disorder. (English) Zbl 1257.82060 J. Stat. Phys. 149, No. 6, 969-1012 (2012). MSC: 82B44 82B20 PDFBibTeX XMLCite \textit{B. Nachtergaele} et al., J. Stat. Phys. 149, No. 6, 969--1012 (2012; Zbl 1257.82060) Full Text: DOI arXiv
Nachtergaele, Bruno; Ng, Stephen; Starr, Shannon Ferromagnetic ordering of energy levels for \(\mathrm{U}_q(\mathfrak{sl}_2)\) symmetric spin chains. (English) Zbl 1251.82011 Lett. Math. Phys. 100, No. 3, 327-356 (2012). MSC: 82B10 82B20 81R50 PDFBibTeX XMLCite \textit{B. Nachtergaele} et al., Lett. Math. Phys. 100, No. 3, 327--356 (2012; Zbl 1251.82011) Full Text: DOI arXiv
Bachmann, Sven; Michalakis, Spyridon; Nachtergaele, Bruno; Sims, Robert Automorphic equivalence within gapped phases of quantum lattice systems. (English) Zbl 1233.82006 Commun. Math. Phys. 309, No. 3, 835-871 (2012). MSC: 82B20 82B26 PDFBibTeX XMLCite \textit{S. Bachmann} et al., Commun. Math. Phys. 309, No. 3, 835--871 (2012; Zbl 1233.82006) Full Text: DOI arXiv
Nachtergaele, Bruno; Schlein, Benjamin; Sims, Robert; Starr, Shannon; Zagrebnov, Valentin On the existence of the dynamics for anharmonic quantum oscillator systems. (English) Zbl 1187.82071 Rev. Math. Phys. 22, No. 2, 207-231 (2010). MSC: 82C10 82C20 81Q15 37K60 46L55 PDFBibTeX XMLCite \textit{B. Nachtergaele} et al., Rev. Math. Phys. 22, No. 2, 207--231 (2010; Zbl 1187.82071) Full Text: DOI arXiv
Hamza, Eman; Michalakis, Spyridon; Nachtergaele, Bruno; Sims, Robert Approximating the ground state of gapped quantum spin systems. (English) Zbl 1248.81013 J. Math. Phys. 50, No. 9, 095213, 16 p. (2009). MSC: 81P40 82B20 PDFBibTeX XMLCite \textit{E. Hamza} et al., J. Math. Phys. 50, No. 9, 095213, 16 p. (2009; Zbl 1248.81013) Full Text: DOI arXiv
Nachtergaele, Bruno; Raz, Hillel; Schlein, Benjamin; Sims, Robert Lieb-Robinson bounds for harmonic and anharmonic lattice systems. (English) Zbl 1196.82074 Commun. Math. Phys. 286, No. 3, 1073-1098 (2009). MSC: 82B20 82B23 46N55 PDFBibTeX XMLCite \textit{B. Nachtergaele} et al., Commun. Math. Phys. 286, No. 3, 1073--1098 (2009; Zbl 1196.82074) Full Text: DOI arXiv
Nachtergaele, Bruno; Sims, Robert A multi-dimensional Lieb-Schultz-Mattis theorem. (English) Zbl 1136.82009 Commun. Math. Phys. 276, No. 2, 437-472 (2007). MSC: 82B20 82D40 PDFBibTeX XMLCite \textit{B. Nachtergaele} and \textit{R. Sims}, Commun. Math. Phys. 276, No. 2, 437--472 (2007; Zbl 1136.82009) Full Text: DOI arXiv Link
Messager, Alain; Nachtergaele, Bruno A model with simultaneous first and second order phase transitions. (English) Zbl 1127.82021 J. Stat. Phys. 122, No. 1, 1-14 (2006). MSC: 82B26 82B05 82B20 PDFBibTeX XMLCite \textit{A. Messager} and \textit{B. Nachtergaele}, J. Stat. Phys. 122, No. 1, 1--14 (2006; Zbl 1127.82021) Full Text: DOI arXiv
Nachtergaele, Bruno The spectral gap for some spin chains with discrete symmetry breaking. (English) Zbl 0838.60091 Commun. Math. Phys. 175, No. 3, 565-606 (1996). MSC: 60K40 82B27 81R40 PDFBibTeX XMLCite \textit{B. Nachtergaele}, Commun. Math. Phys. 175, No. 3, 565--606 (1996; Zbl 0838.60091) Full Text: DOI arXiv
Aizenman, Michael; Nachtergaele, Bruno Geometric aspects of quantum spin states. (English) Zbl 0799.58087 Commun. Math. Phys. 164, No. 1, 17-63 (1994). MSC: 58Z05 82D45 82B10 PDFBibTeX XMLCite \textit{M. Aizenman} and \textit{B. Nachtergaele}, Commun. Math. Phys. 164, No. 1, 17--63 (1994; Zbl 0799.58087) Full Text: DOI arXiv
Fannes, M.; Nachtergaele, B.; Werner, R. F. Finitely correlated states on quantum spin chains. (English) Zbl 0755.46039 Commun. Math. Phys. 144, No. 3, 443-490 (1992). Reviewer: A.Wehrl (Wien) MSC: 46N50 82B10 82B20 PDFBibTeX XMLCite \textit{M. Fannes} et al., Commun. Math. Phys. 144, No. 3, 443--490 (1992; Zbl 0755.46039) Full Text: DOI