# Physics 250 (Fall 2013) ### Phy250 (Fall 2013) Sort **"Demystifying" Quantum Field Theory** **Classes**: *Lectures* Tu-Thu 2:00-3:30pm, Leconte 385. *Discussion Session* (by announcement). **Office Hours**: (to appear). **Outline:** This is a special topics course aimed at graduate students interested either in modern condensed matter theory or high energy physics. The central theme of this course will be to demonstrate how field theory is often the natural tool to describe a wide range of quantum systems, and the bag of tricks that can be employed to study them. We will discuss a number of different lattice models and show how the long distance physics is naturally described in terms of a field theory. Techniques such as low and high temperature expansion, large-N techniques, as well as the renormalization group, dualities and exact solutions will be discussed. These will be applied to models of spontaneous symmetry breaking describing superfluidity and magnetism. We will also discuss exotic phases with topological order, such as fractional quantum Hall states and spin liquids and how they can be naturally described by gauge theories. **Suggested Books:** 1. Gauge Fields and Strings: A. Polyakov 2. Quantum Field Theory of Many Body Systems: X. G. Wen 3. Quantum Phase Transitions. Subir Sachdev. **Evaluation** 35% Assignments, 10% Class participation, 55% Final Project [for 2 credits, no final project] Problem Set 1:[\[Due Oct 31\]](https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxhc2h2aW52aXNofGd4OjEzOGVlMDU0OWQzZjM2NmQ) Solutions: Problems 1,2 [\[Sol. Part 1\]](https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxhc2h2aW52aXNofGd4OjI5MGM3MzBjZDA2NWQ2N2Q) Remaining problems [\[Sol. Part 2\]](https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxhc2h2aW52aXNofGd4OjM4MzA2ZTlkMWQ0MmE3MmE) Problem Set 2:[ \[Due Dec 9\]](https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxhc2h2aW52aXNofGd4OjQwMzg4ODE2ZDk0MjU5NTE) Solutions: [\[Soln PS2\]](https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxhc2h2aW52aXNofGd4OjE5ODc1MzRmOGQ0YjlkYTM) *Pick up graded problem sets from Itamar Kimchi in Birge 521 on Wednesday, Dec 18* **[PROJECT TOPICS:](https://sites.google.com/site/ashvinvishwanath/Home/https-sites-google-com-site-ashvinvish-phy250_new/project-topics)** **Lecture Notes (FALL 2013)**- **Sep 3, 5:** Transverse Field Ising Chain in D=1+1. - [Lecture 2: Phase diagram and duality.](https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxhc2h2aW52aXNofGd4OjEwODFlYTczMTc3MGY4ZmM) - Lecture 3: - Lecture Notes: [Correlation Functions and Physical Realization ](https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxhc2h2aW52aXNofGd4OjE2ZjRlNjRhOGZiOTA3NzU) - [Powerpoint summary of experiments (Coldea et al. Science 2000).](https://sites.google.com/site/ashvinvishwanath/phy250/ColdeaExptTransverse_Ising.pdf?attredirects=0&attachauth=ANoY7cp9OOTeDg8QCoLQeGmcGQdp2WJ2Ywb5JWrqJe2j3CAduKlU7HNPYi_Yne5LoHiPSJKvPX64MXX4oyXbI_TpQUYrayfNbDZHLGNI2fSREZBPieA0B_y4eo2RjpsWDpXR3f3dfHSmo9cka_9yTQzNqysvt8JQrLo4F4aiCminkV-wtDiu5vlgkyB02kyzpglVsGs0y_O7r_wqtsNh40XvYfAW8qkTVQ-w3RYyL0e4sUPB_Ra2YUmH46aJ6YaM8h5zsl9-XvYQ) - **Sep 10, 12:** Transverse Field Ising Chain in D=1+1. - Lecture 4: [Exact Solution via Fermions.](https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxhc2h2aW52aXNofGd4OjU0MzBhODllYTg0YWJlNDU) - Lecture 5: [Scale invariance at the transition](https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxhc2h2aW52aXNofGd4OjUxYWVlZmFhYzU2NjdlMGM&pli=1) - **Sep 17** - Lecture 6: [Quantum to Classical Mapping](https://sites.google.com/site/ashvinvishwanath/Home/phy216/QuantumToClassical.pdf?attredirects=0&attachauth=ANoY7coFzgWTrBj-PoAfQx7lBWGWHCtDlYbHio_LPdChw4TrIL7mBg4PEQ7lI0BDyVFTLsLlsp4mv0E4eEa2F_nSB02a6_jjvVZmywamNhmeWgvFSHyCu8Tgg5b9wZng41GFuKD9F6zEKc720Ak5uYyDMCgs-ASDuSnl6Ikd0nYHa1xPJGbadECHx78PLyCtnCjJEI71X6jLsDgVsd7_OA2n1R5ADpnDsekOw6dBeSB-HGoVumncFr0=) - **Sep 19, 24:** Spontaneous breaking of continuous Symmetry - Superfluidity - Basic concepts [(Anderson Review)](http://rmp.aps.org/pdf/RMP/v38/i2/p298_1) - Bose-Hubbard Model and Superfluid-Insulator transition [(NOTES)](https://sites.google.com/site/ashvinvishwanath/phy250/BoseHubbardModel.pdf?attredirects=0&attachauth=ANoY7cpajE2wWYQVpHFmktJ1ae0zR9JyxHl-FCtWyrUM4hc2XlSiEHirAwausTlqcYKb-cYqW1shYcj-1PC9mVKzkQOpAb7OzjJ0qfob8QXP7yo3FeFADu_Sh-DwXNXIG4gBlCJ-KuW1K7ltoML46xFmaCzgDlpzf66OGzsDPotgZGZr1sVWwLBm-2QSD0Y9RBehEmSbAcgmfdMGNulKJmXYVgKk5TVtEW6K6ADnCZ3_Y8m1Tr8aWYM=) - **Sep 26, Oct 1:** Superfluid - Superconductor Duality and Transition: - Anderson Tower: [NOTES](https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxhc2h2aW52aXNofGd4OjU2MGE2NjZiZGQxZjk5OQ) - Duality in 2+1D: [NOTES](https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxhc2h2aW52aXNofGd4OmQxMjc4MWVlYTMyNzEz) - Transition in the large N limit: [NOTES](https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxhc2h2aW52aXNofGd4OjJjMmE4OGZkZTk3MTE1ZTA) - **Oct 3, 8, 10:** Superfluids and Insulators in 1+1 Dimension - Duality and Phases of 1+1 D Bose Hubbard model. [NOTES](https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxhc2h2aW52aXNofGd4OjIyNWE5MWRhMjdiOTc0MjY) - 1+1 D Bose Hubbard Model at Half Filling. Role of Berry Phases. - **Oct 15-29:** Gauge Theories in Condensed Matter Physics: - Z2 gauge theories. Confinement and Deconfinement. [NOTES](https://sites.google.com/site/ashvinvishwanath/phy250/DualityIsingGaugeTheory.pdf?attredirects=0&attachauth=ANoY7cpO-t6zeMg9BKAlSaR3ABVx6GXYCqcBfJ6japvTYv2oltDjc2TNiBvkssWZzxwKPFMrZbyx4p3rdwfFIuNWWl99cJObxfnj3TMhyrIJ-4suF96yTocRsKPXyMfu0wtn8Y2fR8KLd8RmwMGqKvAeIDeIpkCOwGNvPPaUL8DfWvL-UDnJk1npQeLUdg-UllZPxBnTrE0BVA-CGMy09bH9jipgc6zcx3Sf1YqoHNZTgn2jcY9-bgY=) - Topological order. [NOTES](https://sites.google.com/site/ashvinvishwanath/phy250/Topological-Order.pdf?attredirects=0&attachauth=ANoY7cqF8hBWzj3M7E1X-ulwRDTbT64wgF1MG8Nx_GTuPrE0OHxy3lPLYTYHiIXt0-FW90JyPGu2sRajGF8yQsxfXQ9GQrJAINTNi4fJ2IqReA9MvgvB18KHaNUMWCTdMUZvrS4O_3yLeXELyQ14IPTyI795SOSHu0E7K6RFpkIgE0rGsh0fWvV2DtATSH4iVZwddpCrZzAzatao5szfgS04zT9TXwUBGpoj9lSwq1crCN-3lNR2wV4=&attredirects=1) - Anyon statisitics in the Toric Code. [Kitaev-Laumann Note on Arxiv](http://xxx.lanl.gov/abs/0904.2771) - topological entanglement entropy [Notes](https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxhc2h2aW52aXNofGd4OjFkOGYxNDZjNDVjMjA4Y2I) - U(1) gauge theories and Polyakov Mechanism \[Origin in Solid State Physics - [Notes](https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxhc2h2aW52aXNofGd4OjYyZmRhNTNjZGU4ODg5MjY)\] - **Oct 31- Dec 3:** Quantum Hall Effects - Integer Quantum Hall effect [Girvin Review](http://xxx.lanl.gov/pdf/cond-mat/9907002v1) - Laughlin Theory of Fractional Quantum Hall Effect [Girvin Review](http://xxx.lanl.gov/pdf/cond-mat/9907002v1) - Fractional Charge and Fractional Statistics [ArovasSchriefferWilczek](http://prl.aps.org/abstract/PRL/v53/i7/p722_1) - Composite Bosons and Fermions [\[Zhang, Kivelson, Hansson\]](http://prl.aps.org/abstract/PRL/v62/i1/p82_1) [\[Jain\]](http://prl.aps.org/abstract/PRL/v63/i2/p199_1)[\[Zhang\]](http://www.worldscientific.com/doi/pdf/10.1142/S0217979292000037) - Chern Simons Theory of Fractional Quantum Hall States \[Wen Book\] - Edge States and Tunneling \[Wen book, [Experimental Review1](http://www.phy.duke.edu/~yingshe/RMP-Preprint.pdf), [Experimental Review2](http://www.lorentz.leidenuniv.nl/beenakkr/mesoscopics/topics/noise/physics_today_2003.pdf)\] - Skyrmions in Quantum Hall \[[Girvin -Physics Today](http://qpt.physics.harvard.edu/girvin_physicstoday.pdf)\]