Advanced Computing Platform for Theoretical Physics

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Commit b9f4300c authored by Pan Zhang's avatar Pan Zhang
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fix an error on ln \lambda_max

parent 44c1245d
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......@@ -62,7 +62,8 @@
"### Autograd of the leading eigenvalue of the transfer matrix\n",
"In the last section, we have evaluated $\\ln Z$ using RG. Actually, this can be evaluated analytically as\n",
"$$\\ln Z =\n",
"\\frac{1}{t}\\lim_{t\\to\\infty}\\ln \\mathrm{tr}(T^t)=\\frac{1}{t}\\lim_{t\\to\\infty}\\sum_{i=1}^N \\lambda_i^t=\\lambda_\\mathrm{max},$$\n",
"\\frac{1}{t}\\lim_{t\\to\\infty}\\ln \\mathrm{tr}(T^t)=\\frac{1}{t}\\lim_{t\\to\\infty}\\ln\\sum_{i=1}^N \\lambda_i^t=\n",
"\\ln\\lambda_\\mathrm{max},$$\n",
"where $\\lambda_{\\mathrm{max}}$ is the leading eigenvalue. Thus we can do back propagation directly on $\\lambda_{\\mathrm{max}}$."
]
},
......
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