Advanced Quantum Matter

PHYS40071 Advanced Quantum Matter 15 Semester 1 Undergraduate Level 7 Department of Physics & Astronomy 1 FHEQ level (Framework for Higher Education Qualifications) ' Undefined ' European Credit Transfer & Accumulation System Rating : 7.5 <span class="TextRun SCXW162518852 BCX0 NormalTextRun" style="-webkit-tap-highlight-color:transparent;-webkit-text-stroke-width:0px;-webkit-user-drag:none;font-style:normal;font-variant-caps:normal;font-variant-ligatures:none !important;font-weight:400;letter-spacing:normal;line-height:18.3458px;margin:0px;orphans:2;padding:0px;text-align:justify;text-decoration-color:initial;text-decoration-style:initial;text-decoration-thickness:initial;text-indent:0px;text-transform:none;user-select:text;white-space:normal;widows:2;word-spacing:0px;" data-contrast="none" xml:lang="EN-GB" lang="EN-GB">This unit offers an advanced introduction to modern quantum Condensed Matter Physics, in particular the physics of topological and strongly correlated quantum systems. <span class="EOP SCXW162518852 BCX0" style="-webkit-tap-highlight-color:transparent;-webkit-text-stroke-width:0px;-webkit-user-drag:none;font-style:normal;font-variant-caps:normal;font-variant-ligatures:normal;font-weight:400;letter-spacing:normal;line-height:18.3458px;margin:0px;orphans:2;padding:0px;text-align:justify;text-decoration-color:initial;text-decoration-style:initial;text-decoration-thickness:initial;text-indent:0px;text-transform:none;user-select:text;white-space:normal;widows:2;word-spacing:0px;" data-ccp-props="{"335551550":6,"335551620":6,"335572071":4,"335572072":1,"335572073":4278190080,"335572075":4,"335572076":6,"335572077":4278190080,"335572079":4,"335572080":1,"335572081":4278190080,"335572083":4,"335572084":4,"335572085":4278190080,"469789798":"single","469789802":"single","469789806":"single","469789810":"single"}">  <span class="TextRun SCXW162518852 BCX0 NormalTextRun" style="-webkit-tap-highlight-color:transparent;-webkit-text-stroke-width:0px;-webkit-user-drag:none;font-style:normal;font-variant-caps:normal;font-variant-ligatures:none !important;font-weight:400;letter-spacing:normal;line-height:18.3458px;margin:0px;orphans:2;padding:0px;text-align:justify;text-decoration-color:initial;text-decoration-style:initial;text-decoration-thickness:initial;text-indent:0px;text-transform:none;user-select:text;white-space:normal;widows:2;word-spacing:0px;" data-contrast="none" xml:lang="EN-GB" lang="EN-GB">This unit offers an advanced introduction to modern quantum Condensed Matter Physics, in particular the physics of topological and strongly correlated quantum systems. <span class="EOP SCXW162518852 BCX0" style="-webkit-tap-highlight-color:transparent;-webkit-text-stroke-width:0px;-webkit-user-drag:none;font-style:normal;font-variant-caps:normal;font-variant-ligatures:normal;font-weight:400;letter-spacing:normal;line-height:18.3458px;margin:0px;orphans:2;padding:0px;text-align:justify;text-decoration-color:initial;text-decoration-style:initial;text-decoration-thickness:initial;text-indent:0px;text-transform:none;user-select:text;white-space:normal;widows:2;word-spacing:0px;" data-ccp-props="{"335551550":6,"335551620":6,"335572071":4,"335572072":1,"335572073":4278190080,"335572075":4,"335572076":6,"335572077":4278190080,"335572079":4,"335572080":1,"335572081":4278190080,"335572083":4,"335572084":4,"335572085":4278190080,"469789798":"single","469789802":"single","469789806":"single","469789810":"single"}">  <span class="TextRun SCXW266907384 BCX0 NormalTextRun" style="-webkit-tap-highlight-color:transparent;-webkit-text-stroke-width:0px;-webkit-user-drag:none;font-style:normal;font-variant-caps:normal;font-variant-ligatures:none !important;font-weight:400;letter-spacing:normal;line-height:18.3458px;margin:0px;orphans:2;padding:0px;text-align:justify;text-decoration-color:initial;text-decoration-style:initial;text-decoration-thickness:initial;text-indent:0px;text-transform:none;user-select:text;white-space:normal;widows:2;word-spacing:0px;" data-contrast="none" xml:lang="EN-GB" lang="EN-GB">This unit aims to provide students with a comprehensive understanding of the theoretical framework underlying modern condensed matter physics, where quantum statistics, topology, and strong correlations play a central role. After introducing the second-quantized formalism for bosons and fermions, the course develops the conceptual and mathematical tools necessary to analyse quantum Hall systems, superconductivity, as well as topological and strongly-correlated phases of matter. Students will develop the ability to connect abstract theoretical constructs to experimentally observable phenomena and to use these ideas to access current research in condensed matter physics.<span class="EOP SCXW266907384 BCX0" style="-webkit-tap-highlight-color:transparent;-webkit-text-stroke-width:0px;-webkit-user-drag:none;font-style:normal;font-variant-caps:normal;font-variant-ligatures:normal;font-weight:400;letter-spacing:normal;line-height:18.3458px;margin:0px;orphans:2;padding:0px;text-align:justify;text-decoration-color:initial;text-decoration-style:initial;text-decoration-thickness:initial;text-indent:0px;text-transform:none;user-select:text;white-space:normal;widows:2;word-spacing:0px;" data-ccp-props="{"335551550":6,"335551620":6,"335572071":4,"335572072":1,"335572073":4278190080,"335572075":4,"335572076":6,"335572077":4278190080,"335572079":4,"335572080":1,"335572081":4278190080,"335572083":4,"335572084":4,"335572085":4278190080,"469789798":"single","469789802":"single","469789806":"single","469789810":"single"}">  ILO 1 - <span class="TextRun SCXW223858007 BCX0 NormalTextRun" style="-webkit-tap-highlight-color:transparent;-webkit-text-stroke-width:0px;-webkit-user-drag:none;font-style:normal;font-variant-caps:normal;font-variant-ligatures:none !important;font-weight:400;letter-spacing:normal;line-height:18.3458px;margin:0px;orphans:2;padding:0px;text-align:justify;text-decoration-color:initial;text-decoration-style:initial;text-decoration-thickness:initial;text-indent:0px;text-transform:none;user-select:text;white-space:normal;widows:2;word-spacing:0px;" data-contrast="auto" xml:lang="EN-GB" lang="EN-GB">Apply advanced theoretical frameworks to model and interpret the behaviour of quantum many-body systems.<span class="EOP SCXW223858007 BCX0" style="-webkit-tap-highlight-color:transparent;-webkit-text-stroke-width:0px;-webkit-user-drag:none;font-style:normal;font-variant-caps:normal;font-variant-ligatures:normal;font-weight:400;letter-spacing:normal;line-height:18.3458px;margin:0px;orphans:2;padding:0px;text-align:justify;text-decoration-color:initial;text-decoration-style:initial;text-decoration-thickness:initial;text-indent:0px;text-transform:none;user-select:text;white-space:normal;widows:2;word-spacing:0px;" data-ccp-props="{"335551550":6,"335551620":6}"> ILO 2 - <span class="TextRun SCXW254353680 BCX0 NormalTextRun" style="-webkit-tap-highlight-color:transparent;-webkit-text-stroke-width:0px;-webkit-user-drag:none;font-style:normal;font-variant-caps:normal;font-variant-ligatures:none !important;font-weight:400;letter-spacing:normal;line-height:18.3458px;margin:0px;orphans:2;padding:0px;text-align:justify;text-decoration-color:initial;text-decoration-style:initial;text-decoration-thickness:initial;text-indent:0px;text-transform:none;user-select:text;white-space:normal;widows:2;word-spacing:0px;" data-contrast="auto" xml:lang="EN-GB" lang="EN-GB">Apply concepts from topology, quantum mechanics, and condensed matter theory to derive and interpret the physical consequences of models describing superconductivity, quantum Hall effects, and topological insulators.<span class="EOP SCXW254353680 BCX0" style="-webkit-tap-highlight-color:transparent;-webkit-text-stroke-width:0px;-webkit-user-drag:none;font-style:normal;font-variant-caps:normal;font-variant-ligatures:normal;font-weight:400;letter-spacing:normal;line-height:18.3458px;margin:0px;orphans:2;padding:0px;text-align:justify;text-decoration-color:initial;text-decoration-style:initial;text-decoration-thickness:initial;text-indent:0px;text-transform:none;user-select:text;white-space:normal;widows:2;word-spacing:0px;" data-ccp-props="{"335551550":6,"335551620":6}"> ILO 3 - <span class="TextRun SCXW1892531 BCX0 NormalTextRun" style="-webkit-tap-highlight-color:transparent;-webkit-text-stroke-width:0px;-webkit-user-drag:none;font-style:normal;font-variant-caps:normal;font-variant-ligatures:none !important;font-weight:400;letter-spacing:normal;line-height:18.3458px;margin:0px;orphans:2;padding:0px;text-align:justify;text-decoration-color:initial;text-decoration-style:initial;text-decoration-thickness:initial;text-indent:0px;text-transform:none;user-select:text;white-space:normal;widows:2;word-spaci <div class="OutlineElement Ltr SCXW249547846 BCX0" style="-webkit-tap-highlight-color:transparent;-webkit-text-stroke-width:0px;-webkit-user-drag:none;background-color:rgb(255, 255, 255);clear:both;color:rgb(0, 0, 0);cursor:text;direction:ltr;font-family:"Segoe UI", "Segoe UI Web", Arial, Verdana, sans-serif;font-size:12px;font-style:normal;font-variant-caps:normal;font-variant-ligatures:normal;font-weight:400;letter-spacing:normal;margin:0px;orphans:2;overflow:visible;padding:0px;position:relative;text-align:start;text-decoration-color:initial;text-decoration-style:initial;text-decoration-thickness:initial;text-indent:0px;text-transform:none;user-select:text;white-space:normal;widows:2;word-spacing:0px;"><p class="Paragraph SCXW249547846 BCX0" style="-webkit-tap-highlight-color:transparent;-webkit-user-drag:none;background-color:transparent;border-left:0.666667px solid rgb(0, 0, 0);border-right:0.666667px solid rgb(0, 0, 0);border-top:0.666667px solid rgb(0, 0, 0);color:windowtext;font-kerning:none;font-style:normal;font-weight:normal;margin:4px 0px 0px;overflow-wrap:break-word;padding:1.33333px 8px 1.33333px 5.33333px;text-align:justify;text-indent:0px;user-select:text;vertical-align:baseline;" data-ccp-border-bottom="0.6666666666666666px solid #000000" data-ccp-padding-bottom="1.3333333333333333px" paraid="1175525091" paraeid="{89452840-067a-46d6-af17-efa0ba5dbdbc}{122}"><span class="TextRun SCXW249547846 BCX0 NormalTextRun" style="-webkit-tap-highlight-color:transparent;-webkit-user-drag:none;font-variant-ligatures:none !important;line-height:18.3458px;margin:0px;padding:0px;user-select:text;" data-contrast="none" xml:lang="EN-GB" lang="EN-GB">1.<span class="TabRun IPSelectionBlob BlobObject DragDrop SCXW249547846 BCX0 TabChar" style="-webkit-tap-highlight-color:transparent;-webkit-user-drag:none;display:inline-block;font-style:normal;font-weight:400;margin:0px;padding:0px;position:relative;text-align:left;text-indent:0px;user-select:text;white-space:pre !important;width:0px;"> <span class="TextRun SCXW249547846 BCX0 NormalTextRun" style="-webkit-tap-highlight-color:transparent;-webkit-user-drag:none;font-variant-ligatures:none !important;line-height:18.3458px;margin:0px;padding:0px;user-select:text;" data-contrast="none" xml:lang="EN-GB" lang="EN-GB">Introduction to Bose and Fermi operators (2 lecture): 1D spin chains and mapping to bosonic and fermionic problems. Jordan-Wigner and Holstein-Primakoff transformations.<span class="EOP SCXW249547846 BCX0" style="-webkit-tap-highlight-color:transparent;-webkit-user-drag:none;line-height:18.3458px;margin:0px;padding:0px;user-select:text;" data-ccp-props="{"335551550":6,"335551620":6,"335572071":4,"335572072":1,"335572073":4278190080,"335572075":4,"335572076":6,"335572077":4278190080,"335572079":4,"335572080":1,"335572081":4278190080,"335572083":4,"335572084":4,"335572085":4278190080,"469789798":"single","469789802":"single","469789806":"single","469789810":"single"}"> </div><div class="OutlineElement Ltr SCXW249547846 BCX0" style="-webkit-tap-highlight-color:transparent;-webkit-text-stroke-width:0px;-webkit-user-drag:none;background-color:rgb(255, 255, 255);clear:both;color:rgb(0, 0, 0);cursor:text;direction:ltr;font Synchronous learning:<ul><li>33 lectures (includes 6h of example classes)</li></ul> Asynchronous learning:Material available online prior to teaching sessions:<ul><li>Schematic summary of key concepts</li><li>Lecture notes</li><li>Lecture slides (if used) </li></ul> 1 Written exam 100% PHYS30602 Advanced Quantum Mechanics Pre-Requisite Compulsory PHYS30151 Condensed Matter Physics Pre-Requisite Compulsory N <div class="ListContainerWrapper SCXW42885269 BCX0" style="-webkit-tap-highlight-color:transparent;-webkit-text-stroke-width:0px;-webkit-user-drag:none;background-color:rgb(255, 255, 255);color:rgb(0, 0, 0);font-family:"Segoe UI", "Segoe UI Web", Arial, Verdana, sans-serif;font-size:12px;font-style:normal;font-variant-caps:normal;font-variant-ligatures:normal;font-weight:400;letter-spacing:normal;margin:0px;orphans:2;padding:0px;position:relative;text-align:start;text-decoration-color:initial;text-decoration-style:initial;text-decoration-thickness:initial;text-indent:0px;text-transform:none;user-select:text;white-space:normal;widows:2;word-spacing:0px;"><ul><li><span class="TextRun SCXW42885269 BCX0 NormalTextRun" style="-webkit-tap-highlight-color:transparent;-webkit-user-drag:none;font-variant-ligatures:none !important;line-height:18.3458px;margin:0px;padding:0px;user-select:text;" data-contrast="none" xml:lang="EN-GB" lang="EN-GB">Coleman, P. Introduction to Many-Body Physics, Cambridge University Press, 2015.</li><li><span class="TextRun SCXW42885269 BCX0 NormalTextRun" style="-webkit-tap-highlight-color:transparent;-webkit-user-drag:none;font-variant-ligatures:none !important;line-height:18.3458px;margin:0px;padding:0px;user-select:text;" data-contrast="none" xml:lang="EN-GB" lang="EN-GB">Altland, A. & Simons, B. Condensed Matter Field Theory, 2nd ed., Cambridge University Press, 2010.</li><li><span class="TextRun SCXW42885269 BCX0 NormalTextRun" style="-webkit-tap-highlight-color:transparent;-webkit-user-drag:none;font-variant-ligatures:none !important;line-height:18.3458px;margin:0px;padding:0px;user-select:text;" data-contrast="none" xml:lang="EN-GB" lang="EN-GB">Girvin, S. M. & Yang, K. Modern Condensed Matter Physics, Cambridge University Press, 2019.</li><li><span class="TextRun SCXW42885269 BCX0 NormalTextRun" style="-webkit-tap-highlight-color:transparent;-webkit-user-drag:none;font-variant-ligatures:none !important;line-height:18.3458px;margin:0px;padding:0px;user-select:text;" data-contrast="none" xml:lang="EN-GB" lang="EN-GB">Bernevig, B. A. & Hughes, T. L. Topological Insulators and Topological Superconductors, Princeton University Press, 2013.</li><li><span class="TextRun SCXW42885269 BCX0 NormalTextRun" style="-webkit-tap-highlight-color:transparent;-webkit-user-drag:none;font-variant-ligatures:none !important;line-height:18.3458px;margin:0px;padding:0px;user-select:text;" data-contrast="none" xml:lang="EN-GB" lang="EN-GB">Wen, X.-G. Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons, Oxford University Press, 2004.</li><li><span class="TextRun SCXW42885269 BCX0 NormalTextRun" style="-w Lectures 33 0 117