Pub Date : 2024-09-05DOI: 10.21468/scipostphyslectnotes.85
Oleg Tchernyshyov
These lecture notes from the 2023 Summer School "Principles and applications of symmetry in magnetism" introduce the reader to the classical field theory of ferromagnets and antiferromagnets.
{"title":"Field theory of collinear and noncollinear magnetic order","authors":"Oleg Tchernyshyov","doi":"10.21468/scipostphyslectnotes.85","DOIUrl":"https://doi.org/10.21468/scipostphyslectnotes.85","url":null,"abstract":"These lecture notes from the 2023 Summer School \"Principles and applications of symmetry in magnetism\" introduce the reader to the classical field theory of ferromagnets and antiferromagnets.","PeriodicalId":21682,"journal":{"name":"SciPost Physics","volume":null,"pages":null},"PeriodicalIF":5.5,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142187385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-04DOI: 10.21468/scipostphys.17.3.072
Jérôme Fournier, Pierre-Olivier Downey, Charles-David Hébert, Maxime Charlebois, André-Marie Tremblay
In recent years, the $T$-linear scattering rate found at low temperatures, defining the strange metal phase of cuprates, has been a subject of interest. Since a wide range of materials have a scattering rate that obeys the equation $ hbar / tau ≈ k_B T$, the idea of a universal Planckian limit on the scattering rate has been proposed. However, there is no consensus on proposed theories yet. In this work, we present our results for the $T$-linear scattering rate in the triangular lattice Hubbard model obtained using the dynamical cluster approximation. We find two regions with $T$-linear scattering rate in the $T$-$p$ phase diagram: one emerges from the pseudogap to correlated Fermi liquid phase transition at low doping, whereas the other is solely caused by large interaction strength at large doping.
{"title":"Two $T$-linear scattering-rate regimes in the triangular lattice Hubbard model","authors":"Jérôme Fournier, Pierre-Olivier Downey, Charles-David Hébert, Maxime Charlebois, André-Marie Tremblay","doi":"10.21468/scipostphys.17.3.072","DOIUrl":"https://doi.org/10.21468/scipostphys.17.3.072","url":null,"abstract":"In recent years, the $T$-linear scattering rate found at low temperatures, defining the strange metal phase of cuprates, has been a subject of interest. Since a wide range of materials have a scattering rate that obeys the equation $ hbar / tau ≈ k_B T$, the idea of a universal Planckian limit on the scattering rate has been proposed. However, there is no consensus on proposed theories yet. In this work, we present our results for the $T$-linear scattering rate in the triangular lattice Hubbard model obtained using the dynamical cluster approximation. We find two regions with $T$-linear scattering rate in the $T$-$p$ phase diagram: one emerges from the pseudogap to correlated Fermi liquid phase transition at low doping, whereas the other is solely caused by large interaction strength at large doping.","PeriodicalId":21682,"journal":{"name":"SciPost Physics","volume":null,"pages":null},"PeriodicalIF":5.5,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142187434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-02DOI: 10.21468/scipostphys.17.3.069
Fabian Eickhoff, Frithjof Anders
In this paper we consider a multi band extension to the periodic Anderson model. We use a single site DMFT(NRG) in order to study the impact of the conduction band mediated effective hopping of the correlated electrons between the correlated orbitals onto the heavy Fermi liquid formation. Whereas the hybridization of a single impurity model with two distinct conduction bands always adds up constructively, $T_{K}propto exp(-mathrm{const}, U/(Gamma_1+Gamma_2))$, we show that this does not have to be the case in lattice models, where, in remarkable contrast, also an low-energy Fermi liquid scale $T_0propto exp(-mathrm{const}, U/(Gamma_1-Gamma_2))$ can emerge due to quantum interference effects in multi band models, where $U$ denotes the local Coulomb matrix element of the correlated orbitals and $Gamma_i$ the local hybridization strength of band $i$. At high symmetry points, heavy Fermi liquid formation is suppressed which is associated with a breakdown of the Kondo effect. This results in an asymptotically scale-invariant (i.e., power-law) spectrum of the correlated orbitals $propto|omega|^{1/3}$, indicating non-Fermi liquid properties of the quantum critical point, and a small Fermi surface including only the light quasi-particles. This orbital selective Mott phase demonstrates the possibility of metallic local criticality within the general framework of ordinary single site DMFT.
{"title":"Kondo breakdown in multi-orbital Anderson lattices induced by destructive hybridization interference","authors":"Fabian Eickhoff, Frithjof Anders","doi":"10.21468/scipostphys.17.3.069","DOIUrl":"https://doi.org/10.21468/scipostphys.17.3.069","url":null,"abstract":"In this paper we consider a multi band extension to the periodic Anderson model. We use a single site DMFT(NRG) in order to study the impact of the conduction band mediated effective hopping of the correlated electrons between the correlated orbitals onto the heavy Fermi liquid formation. Whereas the hybridization of a single impurity model with two distinct conduction bands always adds up constructively, $T_{K}propto exp(-mathrm{const}, U/(Gamma_1+Gamma_2))$, we show that this does not have to be the case in lattice models, where, in remarkable contrast, also an low-energy Fermi liquid scale $T_0propto exp(-mathrm{const}, U/(Gamma_1-Gamma_2))$ can emerge due to quantum interference effects in multi band models, where $U$ denotes the local Coulomb matrix element of the correlated orbitals and $Gamma_i$ the local hybridization strength of band $i$. At high symmetry points, heavy Fermi liquid formation is suppressed which is associated with a breakdown of the Kondo effect. This results in an asymptotically scale-invariant (i.e., power-law) spectrum of the correlated orbitals $propto|omega|^{1/3}$, indicating non-Fermi liquid properties of the quantum critical point, and a small Fermi surface including only the light quasi-particles. This orbital selective Mott phase demonstrates the possibility of metallic local criticality within the general framework of ordinary single site DMFT.","PeriodicalId":21682,"journal":{"name":"SciPost Physics","volume":null,"pages":null},"PeriodicalIF":5.5,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142187435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-02DOI: 10.21468/scipostphys.17.3.071
Avi Vadali, Zongyuan Wang, Arpit Dua, Wilbur Shirley, Xie Chen
Flux binding is a mechanism that is well-understood for global symmetries. Given two systems, each with a global symmetry, gauging the composite symmetry instead of individual symmetries corresponds to the condensation of the composite of gauge charges belonging to individually gauged theories and the binding of the gauge fluxes. The condensed composite charge is created by a "short" string given by the new minimal coupling corresponding to the composite symmetry. This paper studies what happens when combined subsystem symmetries are gauged, especially when the component charges and fluxes have different sub-dimensional mobilities. We investigate $3+1$D systems with planar symmetries where, for example, the planar symmetry of a planon charge is combined with one of the planar symmetries of a fracton charge. We propose the principle of $textit{Remote Detectability}$ to determine how the fluxes bind and potentially change their mobility. This understanding can then be used to design fracton models with sub-dimensional excitations that are decorated with excitations having nontrivial statistics or non-abelian fusion rules.
{"title":"Composite subsystem symmetries and decoration of sub-dimensional excitations","authors":"Avi Vadali, Zongyuan Wang, Arpit Dua, Wilbur Shirley, Xie Chen","doi":"10.21468/scipostphys.17.3.071","DOIUrl":"https://doi.org/10.21468/scipostphys.17.3.071","url":null,"abstract":"Flux binding is a mechanism that is well-understood for global symmetries. Given two systems, each with a global symmetry, gauging the composite symmetry instead of individual symmetries corresponds to the condensation of the composite of gauge charges belonging to individually gauged theories and the binding of the gauge fluxes. The condensed composite charge is created by a \"short\" string given by the new minimal coupling corresponding to the composite symmetry. This paper studies what happens when combined subsystem symmetries are gauged, especially when the component charges and fluxes have different sub-dimensional mobilities. We investigate $3+1$D systems with planar symmetries where, for example, the planar symmetry of a planon charge is combined with one of the planar symmetries of a fracton charge. We propose the principle of $textit{Remote Detectability}$ to determine how the fluxes bind and potentially change their mobility. This understanding can then be used to design fracton models with sub-dimensional excitations that are decorated with excitations having nontrivial statistics or non-abelian fusion rules.","PeriodicalId":21682,"journal":{"name":"SciPost Physics","volume":null,"pages":null},"PeriodicalIF":5.5,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142187436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-02DOI: 10.21468/scipostphys.17.3.070
Paul B. Fischer, Gianluigi Catelani
Many superconducting devices rely on the finite gap in the excitation spectrum of a superconductor: thanks to this gap, at temperatures much smaller than the critical one the number of excitations (quasiparticles) that can impact the device's behavior is exponentially small. Nevertheless, experiments at low temperature usually find a finite, non-negligible density of quasiparticles whose origin has been attributed to various non-equilibrium phenomena. Here, we investigate the role of photons with energy exceeding the pair-breaking threshold $2Delta$ as a possible source for these quasiparticles in superconducting resonators. Modeling the interacting system of quasiparticles, phonons, sub-gap and pair-breaking photons using a kinetic equation approach, we find analytical expressions for the quasiparticles' density and their energy distribution. Applying our theory to measurements of quality factor as function of temperature and for various readout powers, we find they could be explained by assuming a small number of photons above the pair-breaking threshold. We also show that frequency shift data can give evidence of quasiparticle heating.
{"title":"Nonequilibrium quasiparticle distribution in superconducting resonators: Effect of pair-breaking photons","authors":"Paul B. Fischer, Gianluigi Catelani","doi":"10.21468/scipostphys.17.3.070","DOIUrl":"https://doi.org/10.21468/scipostphys.17.3.070","url":null,"abstract":"Many superconducting devices rely on the finite gap in the excitation spectrum of a superconductor: thanks to this gap, at temperatures much smaller than the critical one the number of excitations (quasiparticles) that can impact the device's behavior is exponentially small. Nevertheless, experiments at low temperature usually find a finite, non-negligible density of quasiparticles whose origin has been attributed to various non-equilibrium phenomena. Here, we investigate the role of photons with energy exceeding the pair-breaking threshold $2Delta$ as a possible source for these quasiparticles in superconducting resonators. Modeling the interacting system of quasiparticles, phonons, sub-gap and pair-breaking photons using a kinetic equation approach, we find analytical expressions for the quasiparticles' density and their energy distribution. Applying our theory to measurements of quality factor as function of temperature and for various readout powers, we find they could be explained by assuming a small number of photons above the pair-breaking threshold. We also show that frequency shift data can give evidence of quasiparticle heating.","PeriodicalId":21682,"journal":{"name":"SciPost Physics","volume":null,"pages":null},"PeriodicalIF":5.5,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142187445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-30DOI: 10.21468/scipostphyscore.7.3.059
Meguya Ryu, Simonas Varapnickas, Darius Gailevicius, Domas Paipulas, Eulalia Puig Vilardell, Zahra Khajehsaeidimahabadi, Saulius Juodkazis, Junko Morikawa, Mangirdas Malinauskas
Determination of refractive index of micro-disks of a calcinated ($1100^circ$C in air) photo-resist SZ2080$^mathrm{TM}$ was carried out using transmission and reflection spectroscopy. Interference fringes at specific wavenumbers/wavelengths were selected for determination of the optical thickness, hence, the refractive index when the thickness of micro-disks was measured by scanning electron microscopy (SEM). Refractive index of disks of $sim 6pm 1~mu$m thickness were determined at visible and IR (2.5-13~$mu$m) spectral ranges and where $2.2pm 0.2$ at visible and IR wavelengths. Peculiarities of optical characterisation of micro-optical structures are discussed in view of possible uncertainties in the definition of geometric parameters, shape and mass density redistribution.
{"title":"Interferometric microscale measurement of refractive index at VIS and IR wavelengths","authors":"Meguya Ryu, Simonas Varapnickas, Darius Gailevicius, Domas Paipulas, Eulalia Puig Vilardell, Zahra Khajehsaeidimahabadi, Saulius Juodkazis, Junko Morikawa, Mangirdas Malinauskas","doi":"10.21468/scipostphyscore.7.3.059","DOIUrl":"https://doi.org/10.21468/scipostphyscore.7.3.059","url":null,"abstract":"Determination of refractive index of micro-disks of a calcinated ($1100^circ$C in air) photo-resist SZ2080$^mathrm{TM}$ was carried out using transmission and reflection spectroscopy. Interference fringes at specific wavenumbers/wavelengths were selected for determination of the optical thickness, hence, the refractive index when the thickness of micro-disks was measured by scanning electron microscopy (SEM). Refractive index of disks of $sim 6pm 1~mu$m thickness were determined at visible and IR (2.5-13~$mu$m) spectral ranges and where $2.2pm 0.2$ at visible and IR wavelengths. Peculiarities of optical characterisation of micro-optical structures are discussed in view of possible uncertainties in the definition of geometric parameters, shape and mass density redistribution.","PeriodicalId":21682,"journal":{"name":"SciPost Physics","volume":null,"pages":null},"PeriodicalIF":5.5,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142187440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-28DOI: 10.21468/scipostphyscodeb.34-r1.3
Manuel Schrauth, Yanick Thurn, Florian Goth, Jefferson Portela, Dietmar Herdt, Felix Dusel
HYPERTILING is a high-performance Python library for the generation and visualization of regular hyperbolic lattices embedded in the Poincaré disk model. Using highly optimized, efficient algorithms, hyperbolic tilings with millions of vertices can be created in a matter of minutes on a single workstation computer. Facilities including computation of adjacent vertices, dynamic lattice manipulation, refinements, as well as powerful plotting and animation capabilities are provided to support advanced uses of hyperbolic graphs. In this manuscript, we present a comprehensive exploration of the package, encompassing its mathematical foundations, usage examples, applications, and a detailed description of its implementation.
{"title":"Codebase release 1.3 for HYPERTILING","authors":"Manuel Schrauth, Yanick Thurn, Florian Goth, Jefferson Portela, Dietmar Herdt, Felix Dusel","doi":"10.21468/scipostphyscodeb.34-r1.3","DOIUrl":"https://doi.org/10.21468/scipostphyscodeb.34-r1.3","url":null,"abstract":"HYPERTILING is a high-performance Python library for the generation and visualization of regular hyperbolic lattices embedded in the Poincaré disk model. Using highly optimized, efficient algorithms, hyperbolic tilings with millions of vertices can be created in a matter of minutes on a single workstation computer. Facilities including computation of adjacent vertices, dynamic lattice manipulation, refinements, as well as powerful plotting and animation capabilities are provided to support advanced uses of hyperbolic graphs. In this manuscript, we present a comprehensive exploration of the package, encompassing its mathematical foundations, usage examples, applications, and a detailed description of its implementation.","PeriodicalId":21682,"journal":{"name":"SciPost Physics","volume":null,"pages":null},"PeriodicalIF":5.5,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142187438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-28DOI: 10.21468/scipostphyscodeb.34
Manuel Schrauth, Yanick Thurn, Florian Goth, Jefferson Portela, Dietmar Herdt, Felix Dusel
HYPERTILING is a high-performance Python library for the generation and visualization of regular hyperbolic lattices embedded in the Poincar'e disk model. Using highly optimized, efficient algorithms, hyperbolic tilings with millions of vertices can be created in a matter of minutes on a single workstation computer. Facilities including computation of adjacent vertices, dynamic lattice manipulation, refinements, as well as powerful plotting and animation capabilities are provided to support advanced uses of hyperbolic graphs. In this manuscript, we present a comprehensive exploration of the package, encompassing its mathematical foundations, usage examples, applications, and a detailed description of its implementation.
{"title":"HYPERTILING — a high performance Python library for the generation and visualization of hyperbolic lattices","authors":"Manuel Schrauth, Yanick Thurn, Florian Goth, Jefferson Portela, Dietmar Herdt, Felix Dusel","doi":"10.21468/scipostphyscodeb.34","DOIUrl":"https://doi.org/10.21468/scipostphyscodeb.34","url":null,"abstract":"HYPERTILING is a high-performance Python library for the generation and visualization of regular hyperbolic lattices embedded in the Poincar'e disk model. Using highly optimized, efficient algorithms, hyperbolic tilings with millions of vertices can be created in a matter of minutes on a single workstation computer. Facilities including computation of adjacent vertices, dynamic lattice manipulation, refinements, as well as powerful plotting and animation capabilities are provided to support advanced uses of hyperbolic graphs. In this manuscript, we present a comprehensive exploration of the package, encompassing its mathematical foundations, usage examples, applications, and a detailed description of its implementation.","PeriodicalId":21682,"journal":{"name":"SciPost Physics","volume":null,"pages":null},"PeriodicalIF":5.5,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142187437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-26DOI: 10.21468/scipostphys.17.2.067
Thomas Bartsch, Mathew Bullimore, Andrea E. V. Ferrari, Jamie Pearson
In this paper we continue our investigation of the global categorical symmetries that arise when gauging finite higher groups and their higher subgroups with discrete torsion. The motivation is to provide a common perspective on the construction of non-invertible global symmetries in higher dimensions and a precise description of the associated symmetry categories. We propose that the symmetry categories obtained by gauging higher subgroups may be defined as higher group-theoretical fusion categories, which are built from the projective higher representations of higher groups. As concrete applications we provide a unified description of the symmetry categories of gauge theories in three and four dimensions based on the Lie algebra $mathfrak{so}(N)$, and a fully categorical description of non-invertible symmetries obtained by gauging a 1-form symmetry with a mixed 't Hooft anomaly. We also discuss the effect of discrete torsion on symmetry categories, based a series of obstructions determined by spectral sequence arguments.
{"title":"Non-invertible symmetries and higher representation theory II","authors":"Thomas Bartsch, Mathew Bullimore, Andrea E. V. Ferrari, Jamie Pearson","doi":"10.21468/scipostphys.17.2.067","DOIUrl":"https://doi.org/10.21468/scipostphys.17.2.067","url":null,"abstract":"In this paper we continue our investigation of the global categorical symmetries that arise when gauging finite higher groups and their higher subgroups with discrete torsion. The motivation is to provide a common perspective on the construction of non-invertible global symmetries in higher dimensions and a precise description of the associated symmetry categories. We propose that the symmetry categories obtained by gauging higher subgroups may be defined as higher group-theoretical fusion categories, which are built from the projective higher representations of higher groups. As concrete applications we provide a unified description of the symmetry categories of gauge theories in three and four dimensions based on the Lie algebra $mathfrak{so}(N)$, and a fully categorical description of non-invertible symmetries obtained by gauging a 1-form symmetry with a mixed 't Hooft anomaly. We also discuss the effect of discrete torsion on symmetry categories, based a series of obstructions determined by spectral sequence arguments.","PeriodicalId":21682,"journal":{"name":"SciPost Physics","volume":null,"pages":null},"PeriodicalIF":5.5,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142187444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-26DOI: 10.21468/scipostphys.17.2.068
Jiunn-Wei Chen, Chang-Tse Hsieh, Ryutaro Matsudo
It is known that the $2+1$d single Majorana fermion theory has an anomaly of the reflection, which is canceled out when 16 copies of the theory are combined. Therefore, it is expected that the reflection symmetric boundary condition is impossible for one Majorana fermion, but possible for 16 Majorana fermions. In this paper, we consider a reflection symmetric boundary condition that varies at a single point, and find that there is a problem with one Majorana fermion. The problem is the absence of a corresponding outgoing wave to a specific incoming wave into the boundary, which leads to the non-conservation of the energy. For 16 Majorana fermions, it is possible to connect every incoming wave to an outgoing wave without breaking the reflection symmetry. In addition, we discuss the connection with the fermion-monopole scattering in $3+1$ dimensions.
{"title":"Boundary condition and reflection anomaly in $2+1$ dimensions","authors":"Jiunn-Wei Chen, Chang-Tse Hsieh, Ryutaro Matsudo","doi":"10.21468/scipostphys.17.2.068","DOIUrl":"https://doi.org/10.21468/scipostphys.17.2.068","url":null,"abstract":"It is known that the $2+1$d single Majorana fermion theory has an anomaly of the reflection, which is canceled out when 16 copies of the theory are combined. Therefore, it is expected that the reflection symmetric boundary condition is impossible for one Majorana fermion, but possible for 16 Majorana fermions. In this paper, we consider a reflection symmetric boundary condition that varies at a single point, and find that there is a problem with one Majorana fermion. The problem is the absence of a corresponding outgoing wave to a specific incoming wave into the boundary, which leads to the non-conservation of the energy. For 16 Majorana fermions, it is possible to connect every incoming wave to an outgoing wave without breaking the reflection symmetry. In addition, we discuss the connection with the fermion-monopole scattering in $3+1$ dimensions.","PeriodicalId":21682,"journal":{"name":"SciPost Physics","volume":null,"pages":null},"PeriodicalIF":5.5,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142187439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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